Packages¶

In [1]:
from selenium import webdriver
from webdriver_manager.chrome import ChromeDriverManager
from selenium.webdriver.chrome.service import Service
from bs4 import BeautifulSoup

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
import plotly.express as px

from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.cluster import KMeans

from sklearn.metrics import calinski_harabasz_score, silhouette_score, davies_bouldin_score

%matplotlib inline

pd.set_option('display.max_columns', None)

Scraping¶

I used Selenium and beautifulsoup to scrape NBA.com. It's important to note that I used the data from the traditional, advanced and scoring pages. Scoring and traditional use this chunk while advanced uses the next chunk. For some reason, the HTML on the advanced page includes things that don't work with this chunk and I had to modify it

In [2]:
def scrape_nba_com(drive, table_name):

    
    soup = BeautifulSoup(drive.page_source, 'html.parser')
    table = soup.find("table", {"class" : table_name}) # Find the table that has table_name
    
    thead = table.find("thead") # Get the head

    # th stands for table-header
    table_headers = thead.find_all("th") # Get all table headers

    # extract actual header name from th elements
    cleaned_headers = [i.text for i in table_headers]

    # more clean up
    cleaned_headers = [i for i in cleaned_headers if "RANK" not in i]
    
    # Get rows
    table_rows = table.find("tbody").find_all("tr")
    
    td_in_rows = [r.find_all("td") for r in table_rows]

    # nested list comprehension to extract actual data from each row
    # code is basically identical to above cell
    table_data = [[td.text for td in i] for i in td_in_rows]
    
    # Change everything into a dataframe
    df = pd.DataFrame(data=table_data, 
             columns=cleaned_headers)
    
    return df
In [3]:
def scrape_nba_com_ad(drive, table_name):
    #driver = webdriver.Chrome(service=Service(ChromeDriverManager().install()))
    #driver.get(url)
    
    soup = BeautifulSoup(drive.page_source, 'html.parser')
    table = soup.find("table", {"class" : table_name})
    
    thead = table.find("thead")

    # th stands for table-header
    table_headers = thead.find_all("th")

    # extract actual header name from th elements
    cleaned_headers = [i.text for i in table_headers]

    # more clean up
    cleaned_headers = [i for i in cleaned_headers if "RANK" not in i]
    
    cleaned_headers = cleaned_headers[:24] # This is the part that is different. Only take columns up to 24
    
    # Get rows
    table_rows = table.find("tbody").find_all("tr")
    
    td_in_rows = [r.find_all("td") for r in table_rows]

    # nested list comprehension to extract actual data from each row
    # code is basically identical to above cell
    # 
    table_data = [[td.text for td in i] for i in td_in_rows]
    
    df = pd.DataFrame(data=table_data, 
             columns=cleaned_headers)
    
    return df

Some important things to note: I only took data from 2022-2023 and I only took traditional, advanced and scoring. In addition, when you run the chunk below, the nba.com page will show up. Click accept for the cookies, and change the drop down arrow that is next to page from 1 to All. This will make it so that all the players show up. Otherwise, you will only get the first 50. This must be done with each of the chunks below that take you to the website. Once you change it to all, minimize the page and run the df_2022 = cell and you should get the dataframe

This one is for traditional

In [4]:
url = "https://www.nba.com/stats/players/traditional?PerMode=PerGame&sort=PTS&dir=-1&SeasonType=Regular+Season&Season=2022-23"
driver = webdriver.Chrome(service=Service(ChromeDriverManager().install()))
driver.get(url)
In [5]:
df_2022 = scrape_nba_com(driver, "Crom_table__p1iZz") # Get the dataframe
In [6]:
df_2022 # Check that it looks correct
Out[6]:
Player Team Age GP W L Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/-
0 1 Joel Embiid PHI 29 66 43 23 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4
1 2 Luka Doncic DAL 24 66 33 33 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9
2 3 Damian Lillard POR 32 58 27 31 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8
3 4 Shai Gilgeous-Alexander OKC 24 68 33 35 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2
4 5 Giannis Antetokounmpo MIL 28 63 47 16 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
534 535 Alondes Williams BKN 23 1 1 0 5.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 0.0 2.0 0.0 0.0 1.0 -0.8 0.0 0.0 -5.0
535 535 Deonte Burton SAC 29 2 1 1 3.2 0.0 0.0 1.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.5
536 535 Frank Jackson UTA 25 1 0 1 5.1 0.0 0.0 3.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 1.0 1.0 2.0 1.0 0.0 0.0 0.0 0.0 3.9 0.0 0.0 -2.0
537 535 Michael Foster Jr. PHI 20 1 1 0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0
538 535 Sterling Brown LAL 28 4 2 2 6.1 0.0 0.0 1.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.8 1.3 2.0 0.5 0.0 0.8 0.0 1.0 5.4 0.0 0.0 -1.0

539 rows × 30 columns

This one is for advanced

In [7]:
url = "https://www.nba.com/stats/players/advanced?PerMode=PerGame&sort=PTS&dir=-1&SeasonType=Regular+Season&Season=2022-23"
driver = webdriver.Chrome(service=Service(ChromeDriverManager().install()))
driver.get(url)
In [8]:
ad_2022 = scrape_nba_com_ad(driver, "Crom_table__p1iZz")
In [9]:
ad_2022
Out[9]:
PLAYER TEAM AGE GP W L MIN OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS
0 A.J. Lawson DAL 22 15 5 10 7.2 96.3 116.4 -20.1 3.2 0.67 3.8 4.6 15.2 9.1 5.8 61.4 58.9 18.9 105.96 7.6 240
1 AJ Green MIL 23 35 27 8 9.9 107.9 112.8 -4.9 9.2 2.44 14.0 1.6 10.5 6.1 5.7 60.0 60.7 15.9 102.90 7.6 744
2 AJ Griffin ATL 19 72 34 38 19.5 113.6 112.0 1.5 7.0 1.74 10.9 2.6 8.0 5.3 6.3 56.0 57.7 17.4 102.67 7.7 3005
3 Aaron Gordon DEN 27 68 45 23 30.2 123.0 110.9 12.1 12.9 2.07 16.9 8.6 13.6 11.2 8.2 60.3 61.7 20.6 100.16 11.2 4288
4 Aaron Holiday ATL 26 63 32 31 13.4 110.8 110.0 0.9 13.5 2.47 24.9 2.8 5.9 4.3 10.1 50.0 52.8 12.9 103.27 5.4 1819
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
534 Zach Collins SAS 25 63 20 43 22.9 108.7 116.3 -7.5 18.0 1.40 19.6 7.6 19.0 13.3 14.0 56.8 59.9 20.9 104.06 11.0 3121
535 Zach LaVine CHI 28 77 38 39 35.9 112.0 111.7 0.3 18.7 1.69 15.7 1.6 10.8 6.4 9.3 55.8 60.7 27.8 99.70 12.6 5750
536 Zeke Nnaji DEN 22 53 34 19 13.7 101.5 107.4 -5.9 4.0 0.58 6.6 8.7 9.9 9.3 11.4 60.5 62.0 14.9 98.40 7.2 1488
537 Ziaire Williams MEM 21 37 21 16 15.2 106.9 112.2 -5.2 8.6 0.95 12.6 2.8 10.5 6.7 13.4 49.2 51.1 17.8 102.80 5.2 1195
538 Zion Williamson NOP 22 29 17 12 33.0 116.2 108.4 7.8 23.1 1.34 16.5 6.0 14.8 10.4 12.3 61.5 65.2 28.8 102.17 17.1 2031

539 rows × 24 columns

This one is for scoring

In [10]:
url = "https://www.nba.com/stats/players/scoring?PerMode=PerGame&sort=PTS&dir=-1&SeasonType=Regular+Season&Season=2022-23"
driver = webdriver.Chrome(service=Service(ChromeDriverManager().install()))
driver.get(url)
In [11]:
score_2022 = scrape_nba_com(driver, "Crom_table__p1iZz")
In [12]:
score_2022
Out[12]:
Player TEAM AGE GP W L MIN %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST
0 A.J. Lawson DAL 22 15 5 10 7.2 43.2 56.8 42.9 0.0 53.6 19.6 3.5 3.6 42.9 50.0 50.0 100 0.0 72.7 27.3
1 AJ Green MIL 23 35 27 8 9.9 16.0 84.0 11.7 5.2 85.7 7.8 2.6 7.1 6.5 77.8 22.2 90.9 9.1 88.7 11.3
2 AJ Griffin ATL 19 72 34 38 19.5 51.4 48.6 46.0 9.7 47.4 10.5 6.6 11.0 36.3 55.8 44.2 89.1 10.9 69.4 30.6
3 Aaron Gordon DEN 27 68 45 23 30.2 77.3 22.7 66.5 2.5 16.2 14.3 17.3 12.6 64.0 63.1 36.9 73.3 26.7 64.6 35.4
4 Aaron Holiday ATL 26 63 32 31 13.4 60.0 40.0 45.3 7.3 43.7 6.9 11.0 13.8 38.1 21.4 78.6 86.1 13.9 46.7 53.3
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
534 Zach Collins SAS 25 63 20 43 22.9 73.2 26.8 62.7 5.7 22.6 4.5 14.7 9.8 56.9 58.1 41.9 100 0.0 66.2 33.8
535 Zach LaVine CHI 28 77 38 39 35.9 60.8 39.2 49.0 12.1 32.0 15.7 19.0 17.0 36.9 33.5 66.5 64.7 35.3 42.9 57.1
536 Zeke Nnaji DEN 22 53 34 19 13.7 66.8 33.2 67.1 0.7 18.4 11.9 14.5 15.9 66.4 72.0 28.0 100 0.0 76.4 23.6
537 Ziaire Williams MEM 21 37 21 16 15.2 50.5 49.5 56.2 6.7 35.7 22.9 8.1 18.6 49.5 78.0 22.0 88.0 12.0 81.0 19.0
538 Zion Williamson NOP 22 29 17 12 33.0 95.9 4.1 73.7 0.3 2.8 11.1 23.5 14.3 73.5 45.7 54.3 85.7 14.3 46.7 53.3

539 rows × 23 columns

In [13]:
# This will merge the dataframes together
data = pd.merge(pd.merge(df_2022, ad_2022, left_on="Player", right_on="PLAYER"), score_2022, on="Player")
In [14]:
data # make sure it worked
Out[14]:
_x Player Team Age GP_x W_x L_x Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- _y PLAYER TEAM_x AGE_x GP_y W_y L_y MIN_x OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS TEAM_y AGE_y GP W L MIN_y %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST
0 1 Joel Embiid PHI 29 66 43 23 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4 Joel Embiid PHI 29 66 43 23 34.6 119.0 110.2 8.8 23.3 1.21 12.7 5.7 24.3 15.7 10.5 57.3 65.5 37.0 97.34 21.3 4639 PHI 29 66 43 23 34.6 84.9 15.1 60.7 15.7 9.1 6.3 30.2 12.7 45.0 60.0 40.0 89.4 10.6 62.6 37.4
1 2 Luka Doncic DAL 24 66 33 33 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9 Luka Doncic DAL 24 66 33 33 36.2 118.1 116.0 2.1 40.8 2.24 21.1 2.4 22.4 12.4 9.4 56.0 60.9 36.8 97.63 20.2 4874 DAL 24 66 33 33 36.2 62.7 37.3 50.0 8.5 26.0 5.2 24.0 14.0 41.4 13.1 86.9 21.6 78.4 15.3 84.7
2 3 Damian Lillard POR 32 58 27 31 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8 Damian Lillard POR 32 58 27 31 36.3 119.5 117.4 2.1 33.8 2.23 20.8 2.2 11.2 6.8 9.3 56.4 64.5 33.1 99.78 17.3 4385 POR 32 58 27 31 36.3 45.3 54.7 33.4 6.0 39.2 8.6 27.4 11.9 27.4 15.7 84.3 51.6 48.4 31.5 68.5
3 4 Shai Gilgeous-Alexander OKC 24 68 33 35 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2 Shai Gilgeous-Alexander OKC 24 68 33 35 35.5 116.1 113.3 2.7 24.9 1.93 16.4 2.3 10.9 6.5 8.5 53.1 62.6 31.8 103.47 17.5 5211 OKC 24 68 33 35 35.5 87.8 12.2 60.5 9.7 8.1 12.7 31.4 17.7 50.8 20.1 79.9 31.0 69.0 21.0 79.0
4 5 Giannis Antetokounmpo MIL 28 63 47 16 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4 Giannis Antetokounmpo MIL 28 63 47 16 32.1 116.4 109.2 7.2 31.4 1.46 16.2 6.5 26.8 17.1 11.1 57.2 60.5 37.3 103.63 20.4 4380 MIL 28 63 47 16 32.1 86.6 13.4 67.4 7.0 7.2 17.5 25.4 12.9 60.3 41.5 58.5 61.7 38.3 42.9 57.1
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
534 535 Alondes Williams BKN 23 1 1 0 5.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 0.0 2.0 0.0 0.0 1.0 -0.8 0.0 0.0 -5.0 Alondes Williams BKN 23 1 1 0 5.3 83.3 136.4 -53.0 0.0 0.00 0.0 0.0 25.0 11.1 100.0 0.0 0.0 14.3 104.81 -10.8 12 BKN 23 1 1 0 5.3 0.0 0.0 0.0 0.0 0.0 0.0 100 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
535 535 Deonte Burton SAC 29 2 1 1 3.2 0.0 0.0 1.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.5 Deonte Burton SAC 29 2 1 1 3.2 164.3 112.5 51.8 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 13.3 110.80 -4.5 14 SAC 29 2 1 1 3.2 50.0 50.0 0.0 0.0 0.0 0.0 100 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
536 535 Frank Jackson UTA 25 1 0 1 5.1 0.0 0.0 3.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 1.0 1.0 2.0 1.0 0.0 0.0 0.0 0.0 3.9 0.0 0.0 -2.0 Frank Jackson UTA 25 1 0 1 5.1 100.0 122.2 -22.2 25.0 0.00 25.0 12.5 33.3 18.2 0.0 0.0 0.0 25.0 85.54 -2.6 9 UTA 25 1 0 1 5.1 66.7 33.3 0.0 0.0 0.0 0.0 100 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
537 535 Michael Foster Jr. PHI 20 1 1 0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2.0 Michael Foster Jr. PHI 20 1 1 0 1.0 0.0 100.0 -100.0 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 92.90 0.0 2 PHI 20 1 1 0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 100 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
538 535 Sterling Brown LAL 28 4 2 2 6.1 0.0 0.0 1.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.8 1.3 2.0 0.5 0.0 0.8 0.0 1.0 5.4 0.0 0.0 -1.0 Sterling Brown LAL 28 4 2 2 6.1 106.8 106.3 0.4 7.7 0.00 33.3 9.1 15.2 12.1 0.0 0.0 0.0 6.1 120.18 3.1 59 LAL 28 4 2 2 6.1 50.0 50.0 0.0 0.0 0.0 0.0 100 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

539 rows × 76 columns

In [15]:
# Drop all duplicate columns and those that are not needed. Could also change the merge above to a different join
data = data.drop(['\xa0_x', '\xa0_y', 'GP_x', 'W_x', 'L_x', 'TEAM_x', 'PLAYER', 'AGE_x', 'GP_y', 'W_y', 'L_y', 'MIN_x', 'TEAM_y', 'AGE_y', 'MIN_y', ' '], axis=1)
In [16]:
data.head() # Make sure everything looks nice
Out[16]:
Player Team Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST
0 Joel Embiid PHI 29 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4 119.0 110.2 8.8 23.3 1.21 12.7 5.7 24.3 15.7 10.5 57.3 65.5 37.0 97.34 21.3 4639 66 43 23 84.9 15.1 60.7 15.7 9.1 6.3 30.2 12.7 45.0 60.0 40.0 89.4 10.6 62.6 37.4
1 Luka Doncic DAL 24 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9 118.1 116.0 2.1 40.8 2.24 21.1 2.4 22.4 12.4 9.4 56.0 60.9 36.8 97.63 20.2 4874 66 33 33 62.7 37.3 50.0 8.5 26.0 5.2 24.0 14.0 41.4 13.1 86.9 21.6 78.4 15.3 84.7
2 Damian Lillard POR 32 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8 119.5 117.4 2.1 33.8 2.23 20.8 2.2 11.2 6.8 9.3 56.4 64.5 33.1 99.78 17.3 4385 58 27 31 45.3 54.7 33.4 6.0 39.2 8.6 27.4 11.9 27.4 15.7 84.3 51.6 48.4 31.5 68.5
3 Shai Gilgeous-Alexander OKC 24 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2 116.1 113.3 2.7 24.9 1.93 16.4 2.3 10.9 6.5 8.5 53.1 62.6 31.8 103.47 17.5 5211 68 33 35 87.8 12.2 60.5 9.7 8.1 12.7 31.4 17.7 50.8 20.1 79.9 31.0 69.0 21.0 79.0
4 Giannis Antetokounmpo MIL 28 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4 116.4 109.2 7.2 31.4 1.46 16.2 6.5 26.8 17.1 11.1 57.2 60.5 37.3 103.63 20.4 4380 63 47 16 86.6 13.4 67.4 7.0 7.2 17.5 25.4 12.9 60.3 41.5 58.5 61.7 38.3 42.9 57.1
In [ ]:
# Write our data to a csv so we don't have to run everything again

#data.to_csv('data.csv', index=False)

Data Exploration¶

In [3]:
df = pd.read_csv('data.csv') # I wrote the data to a csv and now I read it in
In [4]:
df.head() # Check that it looks correct
Out[4]:
Player Team Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST
0 Joel Embiid PHI 29 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4 119.0 110.2 8.8 23.3 1.21 12.7 5.7 24.3 15.7 10.5 57.3 65.5 37.0 97.34 21.3 4639 66 43 23 84.9 15.1 60.7 15.7 9.1 6.3 30.2 12.7 45.0 60.0 40.0 89.4 10.6 62.6 37.4
1 Luka Doncic DAL 24 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9 118.1 116.0 2.1 40.8 2.24 21.1 2.4 22.4 12.4 9.4 56.0 60.9 36.8 97.63 20.2 4874 66 33 33 62.7 37.3 50.0 8.5 26.0 5.2 24.0 14.0 41.4 13.1 86.9 21.6 78.4 15.3 84.7
2 Damian Lillard POR 32 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8 119.5 117.4 2.1 33.8 2.23 20.8 2.2 11.2 6.8 9.3 56.4 64.5 33.1 99.78 17.3 4385 58 27 31 45.3 54.7 33.4 6.0 39.2 8.6 27.4 11.9 27.4 15.7 84.3 51.6 48.4 31.5 68.5
3 Shai Gilgeous-Alexander OKC 24 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2 116.1 113.3 2.7 24.9 1.93 16.4 2.3 10.9 6.5 8.5 53.1 62.6 31.8 103.47 17.5 5211 68 33 35 87.8 12.2 60.5 9.7 8.1 12.7 31.4 17.7 50.8 20.1 79.9 31.0 69.0 21.0 79.0
4 Giannis Antetokounmpo MIL 28 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4 116.4 109.2 7.2 31.4 1.46 16.2 6.5 26.8 17.1 11.1 57.2 60.5 37.3 103.63 20.4 4380 63 47 16 86.6 13.4 67.4 7.0 7.2 17.5 25.4 12.9 60.3 41.5 58.5 61.7 38.3 42.9 57.1
In [5]:
df.info() # Just to make sure that we have no null values, which we don't

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 539 entries, 0 to 538
Data columns (total 60 columns):
 #   Column      Non-Null Count  Dtype  
---  ------      --------------  -----  
 0   Player      539 non-null    object 
 1   Team        539 non-null    object 
 2   Age         539 non-null    int64  
 3   Min         539 non-null    float64
 4   PTS         539 non-null    float64
 5   FGM         539 non-null    float64
 6   FGA         539 non-null    float64
 7   FG%         539 non-null    float64
 8   3PM         539 non-null    float64
 9   3PA         539 non-null    float64
 10  3P%         539 non-null    float64
 11  FTM         539 non-null    float64
 12  FTA         539 non-null    float64
 13  FT%         539 non-null    float64
 14  OREB        539 non-null    float64
 15  DREB        539 non-null    float64
 16  REB         539 non-null    float64
 17  AST         539 non-null    float64
 18  TOV         539 non-null    float64
 19  STL         539 non-null    float64
 20  BLK         539 non-null    float64
 21  PF          539 non-null    float64
 22  FP          539 non-null    float64
 23  DD2         539 non-null    float64
 24  TD3         539 non-null    float64
 25  +/-         539 non-null    float64
 26  OFFRTG      539 non-null    float64
 27  DEFRTG      539 non-null    float64
 28  NETRTG      539 non-null    float64
 29  AST%        539 non-null    float64
 30  AST/TO      539 non-null    float64
 31  AST RATIO   539 non-null    float64
 32  OREB%       539 non-null    float64
 33  DREB%       539 non-null    float64
 34  REB%        539 non-null    float64
 35  TO RATIO    539 non-null    float64
 36  EFG%        539 non-null    float64
 37  TS%         539 non-null    float64
 38  USG%        539 non-null    float64
 39  PACE        539 non-null    float64
 40  PIE         539 non-null    float64
 41  POSS        539 non-null    int64  
 42  GP          539 non-null    int64  
 43  W           539 non-null    int64  
 44  L           539 non-null    int64  
 45  %FGA2PT     539 non-null    float64
 46  %FGA3PT     539 non-null    float64
 47  %PTS2PT     539 non-null    float64
 48  %PTS2PT MR  539 non-null    float64
 49  %PTS3PT     539 non-null    float64
 50  %PTSFBPs    539 non-null    float64
 51  %PTSFT      539 non-null    float64
 52  %PTSOFFTO   539 non-null    float64
 53  %PTSPITP    539 non-null    float64
 54  2FGM%AST    539 non-null    float64
 55  2FGM%UAST   539 non-null    float64
 56  3FGM%AST    539 non-null    float64
 57  3FGM%UAST   539 non-null    float64
 58  FGM%AST     539 non-null    float64
 59  FGM%UAST    539 non-null    float64
dtypes: float64(53), int64(5), object(2)
memory usage: 252.8+ KB
In [6]:
df.describe() # Look at some descriptive statistics
Out[6]:
Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST
count 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000 539.000000
mean 26.053803 19.796846 9.121336 3.348980 7.104824 46.325232 0.990538 2.782560 31.530612 1.434694 1.856957 71.993506 0.866234 2.676809 3.543228 2.068831 1.103711 0.609647 0.382375 1.687941 18.330427 4.011132 0.220779 -0.375139 109.877180 111.433395 -1.555288 13.700742 1.819555 17.541929 4.495176 13.224304 8.822263 10.252319 53.187941 56.058442 17.893135 101.723840 8.835807 2319.506494 48.040816 24.018553 24.022263 59.598330 40.031169 50.936735 6.299443 34.061781 12.430241 15.001484 14.907792 44.634694 53.777365 43.255102 80.663080 10.432282 65.272542 33.615028
std 4.314633 9.539535 6.842216 2.436261 4.956886 10.967271 0.872442 2.244579 13.711120 1.545867 1.880916 21.280275 0.747543 1.773074 2.346968 1.932954 0.826909 0.398533 0.384414 0.792286 11.652091 8.770932 1.564432 3.166926 9.728805 7.555920 12.470820 8.667679 1.124435 8.363304 3.562915 5.740101 4.051268 6.032949 10.618005 10.303772 5.672946 3.538229 4.097701 1726.672874 24.650686 14.496366 13.445866 22.145153 21.980182 20.839758 7.429529 22.246019 10.036057 11.474000 6.961117 21.439216 22.183506 21.466402 29.034435 14.710900 19.759378 18.844581
min 19.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 -0.800000 0.000000 0.000000 -29.000000 0.000000 60.000000 -100.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 85.540000 -10.800000 2.000000 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
25% 23.000000 12.450000 4.150000 1.600000 3.400000 41.650000 0.300000 1.000000 28.100000 0.500000 0.600000 66.700000 0.300000 1.400000 1.800000 0.800000 0.500000 0.300000 0.100000 1.200000 9.650000 0.000000 0.000000 -1.900000 107.100000 109.200000 -6.100000 7.400000 1.150000 11.900000 1.900000 9.350000 6.000000 7.800000 49.450000 52.350000 13.900000 99.760000 6.700000 699.000000 30.500000 12.000000 14.000000 45.100000 26.000000 38.000000 1.100000 17.600000 7.350000 9.500000 11.800000 30.400000 38.600000 28.600000 74.900000 0.000000 53.000000 20.100000
50% 25.000000 19.200000 7.000000 2.700000 5.800000 45.500000 0.800000 2.400000 34.200000 0.900000 1.200000 76.300000 0.700000 2.300000 3.000000 1.400000 0.900000 0.600000 0.300000 1.600000 15.300000 0.000000 0.000000 -0.200000 111.100000 112.200000 -0.600000 11.400000 1.670000 16.400000 3.400000 12.000000 7.900000 9.900000 53.800000 56.700000 17.200000 101.670000 8.600000 2066.000000 54.000000 25.000000 25.000000 59.100000 40.800000 50.000000 4.500000 33.800000 11.300000 13.400000 14.700000 41.800000 56.800000 41.300000 93.100000 4.000000 67.100000 31.700000
75% 29.000000 28.350000 12.100000 4.500000 9.450000 50.600000 1.500000 4.100000 38.500000 1.850000 2.400000 84.100000 1.100000 3.500000 4.500000 2.750000 1.500000 0.800000 0.500000 2.200000 25.100000 3.000000 0.000000 1.350000 114.300000 115.300000 3.300000 18.400000 2.300000 21.650000 6.100000 16.350000 11.100000 11.700000 57.600000 60.900000 20.600000 103.225000 10.900000 3879.500000 68.000000 36.000000 34.000000 73.600000 54.650000 64.950000 8.750000 48.700000 15.800000 18.200000 17.450000 58.550000 69.050000 58.450000 100.000000 14.550000 79.350000 45.600000
max 42.000000 40.800000 33.100000 11.200000 22.200000 100.000000 4.900000 11.400000 100.000000 10.000000 12.300000 100.000000 5.100000 9.600000 12.500000 10.700000 4.100000 3.000000 3.000000 5.000000 56.800000 65.000000 29.000000 9.300000 175.000000 163.600000 95.000000 45.700000 11.000000 58.300000 25.000000 40.000000 25.600000 100.000000 100.000000 106.400000 50.000000 127.290000 36.500000 6079.000000 83.000000 57.000000 60.000000 100.000000 100.000000 100.000000 66.700000 100.000000 100.000000 100.000000 66.700000 100.000000 100.000000 100.000000 100.000000 100.000000 100.000000 100.000000

We can already see some important things from the descriptive statistics. The first thing is that there are many variables whose minimum is 0. This means a player averaged 0 points per game or 0 free throw attempts per game, or whatever the variable may be. That's not going to help us, because it means those players are generally "garbage time players". They only play in the last few minutes when the score is lopsided. Even worse is a NETRTG of -100 or a PIE of -10.8. These are outliers caused by a lack of playing time and they could affect what we are trying to do. I will filter out those that don't play enough. The second thing is that there doesn't seem to be any data errors. There's no negative numbers where there shouldn't be or things of that nature. The third thing is that these variables are on different scales. We may need to standardize or normalize later on.

Correlations¶

Let's look at the pairwise correlations and see what variables are highly correlated

In [7]:
correlations = df.corr()
correlations
Out[7]:
Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST
Age 1.000000 0.141465 0.106178 0.093927 0.087601 0.069254 0.154838 0.136059 0.103236 0.086528 0.070279 0.130108 -0.010731 0.115184 0.083177 0.171299 0.079445 0.086499 0.026236 0.083763 0.131073 0.073168 0.037615 0.203539 0.165613 -0.006589 0.132952 0.145083 0.157116 0.195219 -0.059278 0.001711 -0.011425 -0.007156 0.124377 0.129556 -0.017307 -0.099569 0.103656 0.108307 0.085892 0.172614 -0.028632 -0.071695 0.090077 -0.089300 0.146203 0.097349 -0.140179 -0.026550 -0.116107 -0.137336 0.015655 0.039718 0.020868 0.013203 0.027992 -0.012590
Min 0.141465 1.000000 0.874386 0.879344 0.883663 0.185107 0.682903 0.696960 0.211986 0.710354 0.708431 0.347905 0.386093 0.750189 0.688285 0.730612 0.786925 0.721082 0.379099 0.752922 0.918150 0.488944 0.194129 0.170033 0.432883 0.356788 0.121676 0.369311 0.184209 0.177022 -0.137951 0.048167 -0.013240 -0.087250 0.220694 0.273186 0.414689 -0.303390 0.428535 0.877030 0.649891 0.589629 0.555768 0.073892 -0.044962 0.014108 0.177274 -0.004497 -0.062308 -0.016905 0.018578 -0.047885 -0.115571 0.305266 0.026122 0.356889 -0.181382 0.289378
PTS 0.106178 0.874386 1.000000 0.991753 0.982070 0.201940 0.702705 0.715586 0.218166 0.900180 0.890223 0.327889 0.304307 0.714216 0.635354 0.722161 0.852160 0.581842 0.327158 0.604013 0.952663 0.555874 0.272061 0.253677 0.385475 0.251745 0.148388 0.439515 0.072220 0.023455 -0.137635 0.097341 0.022448 -0.098331 0.210333 0.291327 0.715835 -0.217161 0.596013 0.767651 0.506893 0.478508 0.413408 0.135628 -0.114121 0.047683 0.248702 -0.089468 -0.039062 0.086858 -0.016638 -0.039999 -0.197412 0.367293 -0.058219 0.506853 -0.315100 0.406371
FGM 0.093927 0.879344 0.991753 1.000000 0.977324 0.249524 0.659124 0.671131 0.191461 0.862378 0.861850 0.299364 0.360724 0.745424 0.676889 0.713027 0.850130 0.581773 0.364302 0.626573 0.959370 0.579334 0.278209 0.241080 0.382224 0.260198 0.140731 0.427103 0.063207 0.018972 -0.090841 0.134623 0.069412 -0.089439 0.236849 0.301693 0.698401 -0.215185 0.603178 0.769704 0.513014 0.482467 0.420363 0.196702 -0.174949 0.120044 0.255441 -0.138863 -0.037951 0.051201 -0.015458 0.027996 -0.174075 0.355391 -0.064089 0.472211 -0.311867 0.408323
FGA 0.087601 0.883663 0.982070 0.977324 1.000000 0.102137 0.745964 0.775336 0.217512 0.842125 0.829402 0.329343 0.241994 0.673827 0.584811 0.741067 0.849196 0.598588 0.269203 0.588238 0.930816 0.499863 0.236845 0.210371 0.367977 0.263714 0.127526 0.466512 0.102980 0.052466 -0.203355 0.045574 -0.046635 -0.122794 0.120320 0.192273 0.721353 -0.218987 0.525808 0.771661 0.506447 0.464970 0.427187 0.079130 -0.055504 0.006700 0.279357 -0.032357 -0.022375 0.050566 -0.011706 -0.090487 -0.241023 0.409555 -0.029832 0.527010 -0.337194 0.426410
FG% 0.069254 0.185107 0.201940 0.249524 0.102137 1.000000 -0.111260 -0.177823 0.043123 0.167621 0.213223 0.049772 0.480525 0.352392 0.420051 0.030367 0.152143 0.048938 0.372583 0.321116 0.258848 0.268598 0.086526 0.088961 0.186923 0.060094 0.109435 -0.111962 -0.155847 -0.160476 0.437493 0.313422 0.438926 0.114673 0.916954 0.874155 0.004980 0.015055 0.485037 0.187085 0.230157 0.216416 0.188630 0.616131 -0.549303 0.625311 0.048810 -0.435936 -0.013374 -0.290526 0.044939 0.590949 0.374713 -0.019165 -0.121650 -0.095382 0.138259 0.105023
3PM 0.154838 0.682903 0.702705 0.659124 0.745964 -0.111260 1.000000 0.981637 0.433537 0.467877 0.416197 0.350332 -0.131135 0.314180 0.194871 0.532010 0.534407 0.456959 -0.030592 0.361620 0.598519 0.124891 0.070578 0.199921 0.318373 0.209821 0.121546 0.301674 0.165752 0.062984 -0.449947 -0.214024 -0.340266 -0.179836 0.116529 0.161128 0.459120 -0.176279 0.254609 0.594304 0.405484 0.404778 0.306983 -0.427402 0.449799 -0.444988 0.168861 0.473784 0.016379 -0.110369 -0.002219 -0.491153 -0.174183 0.295590 0.113869 0.463847 -0.079265 0.150268
3PA 0.136059 0.696960 0.715586 0.671131 0.775336 -0.177823 0.981637 1.000000 0.367110 0.496895 0.446703 0.362414 -0.137714 0.328019 0.203036 0.554115 0.560261 0.467127 -0.031571 0.367323 0.612666 0.140196 0.080657 0.184224 0.313021 0.206793 0.119247 0.323465 0.167302 0.065453 -0.468885 -0.213678 -0.349825 -0.197065 0.027589 0.080920 0.498755 -0.175473 0.235118 0.605785 0.406479 0.392165 0.322406 -0.438002 0.462237 -0.435696 0.176347 0.451638 0.027958 -0.084307 0.000845 -0.484758 -0.201537 0.318662 0.119421 0.476755 -0.109815 0.175289
3P% 0.103236 0.211986 0.218166 0.191461 0.217512 0.043123 0.433537 0.367110 1.000000 0.117932 0.072982 0.248766 -0.230716 0.022567 -0.055375 0.175239 0.143592 0.165712 -0.124196 0.089520 0.152959 -0.061319 0.039103 0.059028 0.155744 0.086691 0.069012 0.134837 0.140851 0.101097 -0.352908 -0.163517 -0.265248 -0.121852 0.300090 0.324806 0.110282 -0.138321 0.183809 0.182613 0.171067 0.174296 0.125709 -0.323310 0.364654 -0.401728 0.051840 0.503311 -0.066224 -0.246186 0.039068 -0.408444 -0.020505 0.107288 0.584347 0.241393 0.151911 -0.023200
FTM 0.086528 0.710354 0.900180 0.862378 0.842125 0.167621 0.467877 0.496895 0.117932 1.000000 0.985847 0.311562 0.281225 0.630862 0.565132 0.647616 0.787414 0.482182 0.312064 0.492492 0.851447 0.560635 0.286735 0.247745 0.320940 0.175941 0.143852 0.429674 0.027996 0.010367 -0.069928 0.126239 0.071258 -0.050107 0.116767 0.245922 0.704996 -0.183652 0.589804 0.631733 0.392619 0.366411 0.324762 0.219283 -0.205254 0.082129 0.197742 -0.224059 -0.062077 0.285242 -0.020497 0.011176 -0.226396 0.339564 -0.120076 0.493395 -0.366770 0.426714
FTA 0.070279 0.708431 0.890223 0.861850 0.829402 0.213223 0.416197 0.446703 0.072982 0.985847 1.000000 0.249894 0.357792 0.669413 0.618707 0.628688 0.789800 0.472599 0.359102 0.514481 0.857341 0.598119 0.303343 0.219547 0.311326 0.201777 0.120652 0.411901 0.003208 -0.007810 0.000765 0.173370 0.135861 -0.034788 0.140846 0.251022 0.695193 -0.178890 0.591538 0.626519 0.392780 0.361620 0.330223 0.281697 -0.267137 0.143710 0.185288 -0.277138 -0.060697 0.276308 -0.019945 0.075335 -0.202141 0.323565 -0.155252 0.469244 -0.361292 0.426745
FT% 0.130108 0.347905 0.327889 0.299364 0.329343 0.049772 0.350332 0.362414 0.248766 0.311562 0.249894 1.000000 -0.021217 0.179896 0.128425 0.246562 0.235274 0.211581 0.055422 0.229036 0.295579 0.079474 0.041074 0.133342 0.299523 0.164010 0.134460 0.124153 0.169846 0.025403 -0.187339 -0.098987 -0.138531 -0.139600 0.128982 0.286234 0.170044 -0.183344 0.222807 0.343386 0.368069 0.330139 0.318860 -0.113781 0.171839 -0.132955 0.065192 0.103377 -0.096920 0.041051 0.229101 -0.151972 0.100670 0.195130 0.256770 0.175276 0.062292 0.088549
OREB -0.010731 0.386093 0.304307 0.360724 0.241994 0.480525 -0.131135 -0.137714 -0.230716 0.281225 0.357792 -0.021217 1.000000 0.684341 0.834514 0.093881 0.293349 0.195129 0.638469 0.561199 0.466433 0.592067 0.154833 0.080565 0.223772 0.207250 0.048879 -0.106940 -0.192423 -0.156650 0.748574 0.535720 0.711123 0.069398 0.310442 0.289777 0.034326 -0.159435 0.350115 0.358589 0.325323 0.273328 0.301741 0.547570 -0.532101 0.488431 -0.137768 -0.486455 -0.180319 0.056030 -0.027428 0.522477 0.247337 -0.134427 -0.181373 -0.179885 0.048466 -0.006011
DREB 0.115184 0.750189 0.714216 0.745424 0.673827 0.352392 0.314180 0.328019 0.022567 0.630862 0.669413 0.179896 0.684341 1.000000 0.972541 0.499720 0.679953 0.459379 0.593703 0.709498 0.837013 0.783909 0.341385 0.219016 0.339764 0.228962 0.126481 0.212342 -0.020477 0.018034 0.242586 0.580617 0.530536 0.017758 0.283055 0.311139 0.370118 -0.218660 0.573347 0.673426 0.506842 0.476880 0.415071 0.315229 -0.296860 0.254667 0.039589 -0.260779 -0.131785 0.043063 -0.057218 0.233679 0.076586 0.074334 -0.061567 0.115015 -0.069850 0.144197
REB 0.083177 0.688285 0.635354 0.676889 0.584811 0.420051 0.194871 0.203036 -0.055375 0.565132 0.618707 0.128425 0.834514 0.972541 1.000000 0.406373 0.605686 0.407788 0.652016 0.713829 0.779791 0.780760 0.307263 0.191439 0.327864 0.237605 0.111889 0.125366 -0.077162 -0.037244 0.422077 0.609204 0.627467 0.035060 0.313507 0.328119 0.290217 -0.215727 0.544821 0.622193 0.486234 0.447302 0.409177 0.412976 -0.394173 0.348680 -0.013234 -0.352234 -0.156709 0.049625 -0.053086 0.343391 0.137180 0.013162 -0.102779 0.029368 -0.036760 0.106847
AST 0.171299 0.730612 0.722161 0.713027 0.741067 0.030367 0.532010 0.554115 0.175239 0.647616 0.628688 0.246562 0.093881 0.499720 0.406373 1.000000 0.831550 0.652683 0.090063 0.463791 0.788550 0.469106 0.387921 0.181743 0.293109 0.196372 0.109925 0.828521 0.414712 0.570004 -0.260903 -0.040228 -0.134178 -0.016668 0.037963 0.100635 0.494615 -0.162441 0.446034 0.576156 0.340179 0.336295 0.261091 0.066875 -0.049294 -0.003249 0.222678 -0.024176 -0.031898 0.052775 -0.021240 -0.080517 -0.425670 0.523654 -0.098820 0.576870 -0.467892 0.546260
TOV 0.079445 0.786925 0.852160 0.850130 0.849196 0.152143 0.534407 0.560261 0.143592 0.787414 0.789800 0.235274 0.293349 0.679953 0.605686 0.831550 1.000000 0.567522 0.276845 0.638223 0.868854 0.559351 0.335870 0.137193 0.278104 0.260382 0.059391 0.617437 0.052111 0.237711 -0.101675 0.131922 0.059715 0.217613 0.116198 0.181782 0.654152 -0.147383 0.469491 0.646323 0.404578 0.358509 0.355206 0.195102 -0.194467 0.112423 0.178602 -0.166132 -0.069403 0.117911 -0.044408 0.047135 -0.302428 0.427283 -0.125464 0.522398 -0.425212 0.500964
STL 0.086499 0.721082 0.581842 0.581773 0.598588 0.048938 0.456959 0.467127 0.165712 0.482182 0.472599 0.211581 0.195129 0.459379 0.407788 0.652683 0.567522 1.000000 0.201542 0.530113 0.684821 0.283126 0.167104 0.180937 0.344651 0.158133 0.172883 0.398148 0.276100 0.351376 -0.165546 -0.053282 -0.105540 -0.059931 0.073198 0.130559 0.257482 -0.215612 0.341881 0.596023 0.414046 0.378905 0.350574 0.035664 -0.010075 -0.024276 0.107104 0.018904 0.009756 0.007439 0.139936 -0.060910 -0.260259 0.324435 -0.014121 0.346934 -0.266962 0.325863
BLK 0.026236 0.379099 0.327158 0.364302 0.269203 0.372583 -0.030592 -0.031571 -0.124196 0.312064 0.359102 0.055422 0.638469 0.593703 0.652016 0.090063 0.276845 0.201542 1.000000 0.520855 0.471399 0.443288 0.061188 0.115206 0.212560 0.120279 0.092874 -0.092911 -0.136011 -0.155361 0.391706 0.380875 0.454647 0.029283 0.252134 0.269752 0.108259 -0.137686 0.342870 0.359320 0.310445 0.288612 0.257987 0.388163 -0.374269 0.351937 -0.047344 -0.357623 -0.170207 0.054157 -0.034144 0.358421 0.223246 -0.124426 -0.086044 -0.107780 0.068285 -0.038397
PF 0.083763 0.752922 0.604013 0.626573 0.588238 0.321116 0.361620 0.367323 0.089520 0.492492 0.514481 0.229036 0.561199 0.709498 0.713829 0.463791 0.638223 0.530113 0.520855 1.000000 0.703732 0.427184 0.136517 0.095060 0.348555 0.316532 0.080074 0.164109 0.001248 0.081502 0.166965 0.227263 0.247239 0.108332 0.288200 0.313451 0.214853 -0.187442 0.269976 0.631287 0.514637 0.433790 0.475816 0.244750 -0.221258 0.199666 -0.013112 -0.170082 -0.143138 -0.032886 0.005814 0.198407 0.097830 0.103337 0.047883 0.071721 -0.023693 0.125993
FP 0.131073 0.918150 0.952663 0.959370 0.930816 0.258848 0.598519 0.612666 0.152959 0.851447 0.857341 0.295579 0.466433 0.837013 0.779791 0.788550 0.868854 0.684821 0.471399 0.703732 1.000000 0.665397 0.329808 0.260219 0.415570 0.264402 0.164159 0.482623 0.138206 0.150552 -0.014777 0.217182 0.161261 -0.072387 0.233156 0.302889 0.604438 -0.246247 0.628636 0.796185 0.545229 0.515402 0.443913 0.224107 -0.198628 0.135543 0.192292 -0.165128 -0.079522 0.073973 -0.014394 0.064932 -0.172276 0.340305 -0.084370 0.436525 -0.300949 0.394651
DD2 0.073168 0.488944 0.555874 0.579334 0.499863 0.268598 0.124891 0.140196 -0.061319 0.560635 0.598119 0.079474 0.592067 0.783909 0.780760 0.469106 0.559351 0.283126 0.443288 0.427184 0.665397 1.000000 0.514980 0.232090 0.223949 0.104231 0.111582 0.289120 -0.000653 0.044902 0.250452 0.459809 0.446507 0.016137 0.175619 0.207475 0.368663 -0.157062 0.506514 0.504705 0.350709 0.352824 0.262576 0.310922 -0.305532 0.239307 0.035567 -0.280752 -0.129537 0.109683 -0.077705 0.220153 -0.036590 0.101178 -0.148219 0.165092 -0.164574 0.199610
TD3 0.037615 0.194129 0.272061 0.278209 0.236845 0.086526 0.070578 0.080657 0.039103 0.286735 0.303343 0.041074 0.154833 0.341385 0.307263 0.387921 0.335870 0.167104 0.061188 0.136517 0.329808 0.514980 1.000000 0.181596 0.118975 0.032664 0.072843 0.321799 0.080508 0.151314 0.033172 0.190450 0.155771 0.014352 0.059209 0.077643 0.217692 -0.045190 0.265024 0.187187 0.106959 0.146937 0.037674 0.093627 -0.091947 0.062766 0.011781 -0.087133 -0.038321 0.054935 -0.021254 0.056841 -0.079160 0.101356 -0.039992 0.156454 -0.127723 0.142270
+/- 0.203539 0.170033 0.253677 0.241080 0.210371 0.088961 0.199921 0.184224 0.059028 0.247745 0.219547 0.133342 0.080565 0.219016 0.191439 0.181743 0.137193 0.180937 0.115206 0.095060 0.260219 0.232090 0.181596 1.000000 0.450487 -0.515240 0.663678 0.093910 0.076671 0.059214 -0.000177 0.047203 0.058232 -0.113271 0.123898 0.174803 0.168016 -0.120899 0.305343 0.276027 0.231111 0.442510 -0.053380 -0.033441 0.050389 -0.042718 -0.101177 0.020576 0.080358 0.037694 -0.003015 -0.006536 -0.031007 0.072220 -0.021278 0.136110 -0.055969 0.065693
OFFRTG 0.165613 0.432883 0.385475 0.382224 0.367977 0.186923 0.318373 0.313021 0.155744 0.320940 0.311326 0.299523 0.223772 0.339764 0.327864 0.293109 0.278104 0.344651 0.212560 0.348555 0.415570 0.223949 0.118975 0.450487 1.000000 -0.025445 0.795575 0.073945 0.053480 0.070264 -0.007090 -0.004201 0.014206 -0.180783 0.226595 0.330474 0.260694 -0.123759 0.337983 0.408410 0.373148 0.391776 0.261719 0.059041 0.059130 0.017087 -0.001807 -0.018886 -0.059495 0.005583 0.022224 0.017162 0.008063 0.118516 0.027437 0.120799 -0.063968 0.097334
DEFRTG -0.006589 0.356788 0.251745 0.260198 0.263714 0.060094 0.209821 0.206793 0.086691 0.175941 0.201777 0.164010 0.207250 0.228962 0.237605 0.196372 0.260382 0.158133 0.120279 0.316532 0.264402 0.104231 0.032664 -0.515240 -0.025445 1.000000 -0.625889 0.094269 0.053942 0.049661 0.077211 0.047718 0.045925 0.126758 0.056873 0.012624 0.004033 -0.151833 -0.109561 0.247599 0.244337 0.115898 0.322996 0.064602 -0.080261 0.010741 0.094712 -0.023834 -0.273729 0.026700 0.001298 -0.022421 0.031791 0.054166 0.045775 0.082255 -0.014693 0.029996
NETRTG 0.132952 0.121676 0.148388 0.140731 0.127526 0.109435 0.121546 0.119247 0.069012 0.143852 0.120652 0.134460 0.048879 0.126481 0.111889 0.109925 0.059391 0.172883 0.092874 0.080074 0.164159 0.111582 0.072843 0.663678 0.795575 -0.625889 1.000000 0.000708 0.009141 0.024777 -0.052475 -0.032109 -0.016763 -0.217629 0.142332 0.250250 0.201123 -0.004644 0.330261 0.168756 0.143224 0.235503 0.008674 0.006794 0.094816 0.006822 -0.058782 -0.000317 0.119638 -0.011774 0.016400 0.026968 -0.013288 0.059837 -0.006123 0.044441 -0.041133 0.057901
AST% 0.145083 0.369311 0.439515 0.427103 0.466512 -0.111962 0.301674 0.323465 0.134837 0.429674 0.411901 0.124153 -0.106940 0.212342 0.125366 0.828521 0.617437 0.398148 -0.092911 0.164109 0.482623 0.289120 0.321799 0.093910 0.073945 0.094269 0.000708 1.000000 0.523037 0.761986 -0.287646 -0.105001 -0.199642 0.030295 -0.115420 -0.074478 0.447669 -0.145246 0.318568 0.245004 0.084290 0.100258 0.046441 0.056102 -0.029798 -0.018400 0.231344 0.007992 -0.030535 0.017924 -0.023052 -0.098144 -0.531034 0.566061 -0.081342 0.564587 -0.515915 0.597266
AST/TO 0.157116 0.184209 0.072220 0.063207 0.102980 -0.155847 0.165752 0.167302 0.140851 0.027996 0.003208 0.169846 -0.192423 -0.020477 -0.077162 0.414712 0.052111 0.276100 -0.136011 0.001248 0.138206 -0.000653 0.080508 0.076671 0.053480 0.053942 0.009141 0.523037 1.000000 0.674596 -0.332908 -0.256875 -0.322073 -0.223700 -0.075759 -0.068249 -0.105039 -0.094665 0.043066 0.118655 0.094866 0.126180 0.037883 -0.179552 0.208245 -0.167999 0.103530 0.248542 0.022469 -0.176749 0.095988 -0.199121 -0.206284 0.278951 0.129007 0.241027 -0.118755 0.220256
AST RATIO 0.195219 0.177022 0.023455 0.018972 0.052466 -0.160476 0.062984 0.065453 0.101097 0.010367 -0.007810 0.025403 -0.156650 0.018034 -0.037244 0.570004 0.237711 0.351376 -0.155361 0.081502 0.150552 0.044902 0.151314 0.059214 0.070264 0.049661 0.024777 0.761986 0.674596 1.000000 -0.257821 -0.187905 -0.244955 0.009624 -0.118594 -0.125127 -0.125611 -0.103250 0.026637 0.076024 0.036676 0.063449 -0.001167 -0.073228 0.109251 -0.103968 0.046679 0.158414 -0.061983 -0.118304 0.022575 -0.117218 -0.375948 0.323669 0.041878 0.244618 -0.234344 0.301080
OREB% -0.059278 -0.137951 -0.137635 -0.090841 -0.203355 0.437493 -0.449947 -0.468885 -0.352908 -0.069928 0.000765 -0.187339 0.748574 0.242586 0.422077 -0.260903 -0.101675 -0.165546 0.391706 0.166965 -0.014777 0.250452 0.033172 -0.000177 -0.007090 0.077211 -0.052475 -0.287646 -0.332908 -0.257821 1.000000 0.521086 0.806027 0.167191 0.224621 0.161376 -0.160629 -0.035100 0.120321 -0.095092 -0.002859 -0.015595 0.011572 0.609756 -0.592998 0.570164 -0.234154 -0.564996 -0.076489 0.059860 -0.023574 0.635393 0.323206 -0.269522 -0.258817 -0.325879 0.119056 -0.109940
DREB% 0.001711 0.048167 0.097341 0.134623 0.045574 0.313422 -0.214024 -0.213678 -0.163517 0.126239 0.173370 -0.098987 0.535720 0.580617 0.609204 -0.040228 0.131922 -0.053282 0.380875 0.227263 0.217182 0.459809 0.190450 0.047203 -0.004201 0.047718 -0.032109 -0.105001 -0.256875 -0.187905 0.521086 1.000000 0.919335 0.147905 0.175132 0.143923 0.104302 0.005398 0.405442 0.060621 0.066473 0.063275 0.053647 0.391610 -0.392438 0.377686 -0.140199 -0.383610 -0.066681 0.057776 -0.075679 0.415706 0.243443 -0.174812 -0.122456 -0.203483 0.076435 -0.070089
REB% -0.011425 -0.013240 0.022448 0.069412 -0.046635 0.438926 -0.340266 -0.349825 -0.265248 0.071258 0.135861 -0.138531 0.711123 0.530536 0.627467 -0.134178 0.059715 -0.105540 0.454647 0.247239 0.161261 0.446507 0.155771 0.058232 0.014206 0.045925 -0.016763 -0.199642 -0.322073 -0.244955 0.806027 0.919335 1.000000 0.174081 0.250060 0.201288 0.005275 0.001926 0.357209 0.016133 0.061804 0.058817 0.049895 0.549176 -0.539655 0.527960 -0.194199 -0.519679 -0.054421 0.048651 -0.066231 0.580501 0.331210 -0.242546 -0.195807 -0.287006 0.120907 -0.098675
TO RATIO -0.007156 -0.087250 -0.098331 -0.089439 -0.122794 0.114673 -0.179836 -0.197065 -0.121852 -0.050107 -0.034788 -0.139600 0.069398 0.017758 0.035060 -0.016668 0.217613 -0.059931 0.029283 0.108332 -0.072387 0.016137 0.014352 -0.113271 -0.180783 0.126758 -0.217629 0.030295 -0.223700 0.009624 0.167191 0.147905 0.174081 1.000000 0.023590 -0.009359 -0.017609 0.122754 -0.258277 -0.098678 -0.082968 -0.093460 -0.051346 0.178528 -0.291301 0.198585 -0.141550 -0.255983 -0.076365 0.135623 -0.058221 0.242068 -0.081048 0.037615 -0.208840 0.000252 -0.196610 0.143277
EFG% 0.124377 0.220694 0.210333 0.236849 0.120320 0.916954 0.116529 0.027589 0.300090 0.116767 0.140846 0.128982 0.310442 0.283055 0.313507 0.037963 0.116198 0.073198 0.252134 0.288200 0.233156 0.175619 0.059209 0.123898 0.226595 0.056873 0.142332 -0.115420 -0.075759 -0.118594 0.224621 0.175132 0.250060 0.023590 1.000000 0.954197 -0.027782 -0.012887 0.462199 0.215968 0.262188 0.266703 0.193137 0.284769 -0.202172 0.301873 0.024681 -0.059407 -0.016516 -0.433099 0.040327 0.284937 0.392743 -0.048286 0.045743 -0.044819 0.303271 -0.021534
TS% 0.129556 0.273186 0.291327 0.301693 0.192273 0.874155 0.161128 0.080920 0.324806 0.245922 0.251022 0.286234 0.289777 0.311139 0.328119 0.100635 0.181782 0.130559 0.269752 0.313451 0.302889 0.207475 0.077643 0.174803 0.330474 0.012624 0.250250 -0.074478 -0.068249 -0.125127 0.161376 0.143923 0.201288 -0.009359 0.954197 1.000000 0.095745 -0.034267 0.573614 0.268354 0.292533 0.290523 0.223088 0.259361 -0.169281 0.248755 0.036528 -0.082956 -0.052410 -0.290967 0.047253 0.229186 0.337876 -0.010654 0.059558 0.012918 0.239762 0.019660
USG% -0.017307 0.414689 0.715835 0.698401 0.721353 0.004980 0.459120 0.498755 0.110282 0.704996 0.695193 0.170044 0.034326 0.370118 0.290217 0.494615 0.654152 0.257482 0.108259 0.214853 0.604438 0.368663 0.217692 0.168016 0.260694 0.004033 0.201123 0.447669 -0.105039 -0.125611 -0.160629 0.104302 0.005275 -0.017609 -0.027782 0.095745 1.000000 -0.056733 0.539191 0.357500 0.146066 0.140026 0.116820 0.109779 -0.078586 0.049148 0.266322 -0.136954 0.068467 0.176264 -0.105585 -0.044664 -0.336992 0.398588 -0.136873 0.528714 -0.453046 0.472688
PACE -0.099569 -0.303390 -0.217161 -0.215185 -0.218987 0.015055 -0.176279 -0.175473 -0.138321 -0.183652 -0.178890 -0.183344 -0.159435 -0.218660 -0.215727 -0.162441 -0.147383 -0.215612 -0.137686 -0.187442 -0.246247 -0.157062 -0.045190 -0.120899 -0.123759 -0.151833 -0.004644 -0.145246 -0.094665 -0.103250 -0.035100 0.005398 0.001926 0.122754 -0.012887 -0.034267 -0.056733 1.000000 -0.191414 -0.299818 -0.281333 -0.288500 -0.204735 0.009373 0.004254 0.046714 -0.054686 -0.043545 0.206638 -0.000420 0.012979 0.064373 0.049072 -0.086627 -0.067789 -0.118438 0.030164 -0.048140
PIE 0.103656 0.428535 0.596013 0.603178 0.525808 0.485037 0.254609 0.235118 0.183809 0.589804 0.591538 0.222807 0.350115 0.573347 0.544821 0.446034 0.469491 0.341881 0.342870 0.269976 0.628636 0.506514 0.265024 0.305343 0.337983 -0.109561 0.330261 0.318568 0.043066 0.026637 0.120321 0.405442 0.357209 -0.258277 0.462199 0.573614 0.539191 -0.191414 1.000000 0.388253 0.268749 0.282877 0.187728 0.286808 -0.230211 0.224409 0.237045 -0.226035 0.004625 0.030655 -0.023429 0.135928 -0.018838 0.179143 -0.067677 0.266234 -0.148897 0.259167
POSS 0.108307 0.877030 0.767651 0.769704 0.771661 0.187085 0.594304 0.605785 0.182613 0.631733 0.626519 0.343386 0.358589 0.673426 0.622193 0.576156 0.646323 0.596023 0.359320 0.631287 0.796185 0.504705 0.187187 0.276027 0.408410 0.247599 0.168756 0.245004 0.118655 0.076024 -0.095092 0.060621 0.016133 -0.098678 0.215968 0.268354 0.357500 -0.299818 0.388253 1.000000 0.880536 0.798682 0.753230 0.081859 -0.059853 0.019601 0.112073 -0.021104 -0.016321 0.005316 0.002416 -0.019952 -0.065315 0.249614 0.026623 0.287573 -0.144785 0.230703
GP 0.085892 0.649891 0.506893 0.513014 0.506447 0.230157 0.405484 0.406479 0.171067 0.392619 0.392780 0.368069 0.325323 0.506842 0.486234 0.340179 0.404578 0.414046 0.310445 0.514637 0.545229 0.350709 0.106959 0.231111 0.373148 0.244337 0.143224 0.084290 0.094866 0.036676 -0.002859 0.066473 0.061804 -0.082968 0.262188 0.292533 0.146066 -0.281333 0.268749 0.880536 1.000000 0.891308 0.872384 0.089531 -0.057966 0.054087 0.013879 -0.007669 -0.031626 -0.083367 0.065297 0.047647 0.093275 0.152519 0.119015 0.137737 0.005317 0.105739
W 0.172614 0.589629 0.478508 0.482467 0.464970 0.216416 0.404778 0.392165 0.174296 0.366411 0.361620 0.330139 0.273328 0.476880 0.447302 0.336295 0.358509 0.378905 0.288612 0.433790 0.515402 0.352824 0.146937 0.442510 0.391776 0.115898 0.235503 0.100258 0.126180 0.063449 -0.015595 0.063275 0.058817 -0.093460 0.266703 0.290523 0.140026 -0.288500 0.282877 0.798682 0.891308 1.000000 0.555932 0.040164 -0.013641 0.014367 0.016147 0.033421 -0.013747 -0.090891 0.044638 0.008259 0.090901 0.121253 0.097203 0.148845 0.017888 0.075885
L -0.028632 0.555768 0.413408 0.420363 0.427187 0.188630 0.306983 0.322406 0.125709 0.324762 0.330223 0.318860 0.301741 0.415071 0.409177 0.261091 0.355206 0.350574 0.257987 0.475816 0.443913 0.262576 0.037674 -0.053380 0.261719 0.322996 0.008674 0.046441 0.037883 -0.001167 0.011572 0.053647 0.049895 -0.051346 0.193137 0.223088 0.116820 -0.204735 0.187728 0.753230 0.872384 0.555932 1.000000 0.120838 -0.091564 0.083670 0.008036 -0.050093 -0.043160 -0.054846 0.071585 0.078449 0.073001 0.148891 0.113396 0.092042 -0.009538 0.112041
%FGA2PT -0.071695 0.073892 0.135628 0.196702 0.079130 0.616131 -0.427402 -0.438002 -0.323310 0.219283 0.281697 -0.113781 0.547570 0.315229 0.412976 0.066875 0.195102 0.035664 0.388163 0.244750 0.224107 0.310922 0.093627 -0.033441 0.059041 0.064602 0.006794 0.056102 -0.179552 -0.073228 0.609756 0.391610 0.549176 0.178528 0.284769 0.259361 0.109779 0.009373 0.286808 0.081859 0.089531 0.040164 0.120838 1.000000 -0.961983 0.906288 0.107542 -0.883348 -0.013812 0.066598 0.058467 0.843660 0.093234 0.133680 -0.342752 -0.061382 -0.282070 0.380810
%FGA3PT 0.090077 -0.044962 -0.114121 -0.174949 -0.055504 -0.549303 0.449799 0.462237 0.364654 -0.205254 -0.267137 0.171839 -0.532101 -0.296860 -0.394173 -0.049294 -0.194467 -0.010075 -0.374269 -0.221258 -0.198628 -0.305532 -0.091947 0.050389 0.059130 -0.080261 0.094816 -0.029798 0.208245 0.109251 -0.592998 -0.392438 -0.539655 -0.291301 -0.202172 -0.169281 -0.078586 0.004254 -0.230211 -0.059853 -0.057966 -0.013641 -0.091564 -0.961983 1.000000 -0.871742 -0.094031 0.915876 0.034851 -0.192410 -0.022665 -0.814764 -0.052922 -0.100613 0.392324 0.073826 0.340071 -0.353513
%PTS2PT -0.089300 0.014108 0.047683 0.120044 0.006700 0.625311 -0.444988 -0.435696 -0.401728 0.082129 0.143710 -0.132955 0.488431 0.254667 0.348680 -0.003249 0.112423 -0.024276 0.351937 0.199666 0.135543 0.239307 0.062766 -0.042718 0.017087 0.010741 0.006822 -0.018400 -0.167999 -0.103968 0.570164 0.377686 0.527960 0.198585 0.301873 0.248755 0.049148 0.046714 0.224409 0.019601 0.054087 0.014367 0.083670 0.906288 -0.871742 1.000000 0.096270 -0.860144 0.122309 -0.148595 0.112691 0.938638 0.192745 0.139458 -0.268679 -0.145979 -0.209775 0.364627
%PTS2PT MR 0.146203 0.177274 0.248702 0.255441 0.279357 0.048810 0.168861 0.176347 0.051840 0.197742 0.185288 0.065192 -0.137768 0.039589 -0.013234 0.222678 0.178602 0.107104 -0.047344 -0.013112 0.192292 0.035567 0.011781 -0.101177 -0.001807 0.094712 -0.058782 0.231344 0.103530 0.046679 -0.234154 -0.140199 -0.194199 -0.141550 0.024681 0.036528 0.266322 -0.054686 0.237045 0.112073 0.013879 0.016147 0.008036 0.107542 -0.094031 0.096270 1.000000 -0.063605 -0.001577 -0.051532 0.043756 -0.252933 -0.172408 0.295634 0.001683 0.211830 -0.236185 0.297817
%PTS3PT 0.097349 -0.004497 -0.089468 -0.138863 -0.032357 -0.435936 0.473784 0.451638 0.503311 -0.224059 -0.277138 0.103377 -0.486455 -0.260779 -0.352234 -0.024176 -0.166132 0.018904 -0.357623 -0.170082 -0.165128 -0.280752 -0.087133 0.020576 -0.018886 -0.023834 -0.000317 0.007992 0.248542 0.158414 -0.564996 -0.383610 -0.519679 -0.255983 -0.059407 -0.082956 -0.136954 -0.043545 -0.226035 -0.021104 -0.007669 0.033421 -0.050093 -0.883348 0.915876 -0.860144 -0.063605 1.000000 -0.026264 -0.376576 -0.038917 -0.813998 -0.046794 -0.080777 0.421201 0.097277 0.410379 -0.339708
%PTSFBPs -0.140179 -0.062308 -0.039062 -0.037951 -0.022375 -0.013374 0.016379 0.027958 -0.066224 -0.062077 -0.060697 -0.096920 -0.180319 -0.131785 -0.156709 -0.031898 -0.069403 0.009756 -0.170207 -0.143138 -0.079522 -0.129537 -0.038321 0.080358 -0.059495 -0.273729 0.119638 -0.030535 0.022469 -0.061983 -0.076489 -0.066681 -0.054421 -0.076365 -0.016516 -0.052410 0.068467 0.206638 0.004625 -0.016321 -0.031626 -0.013747 -0.043160 -0.013812 0.034851 0.122309 -0.001577 -0.026264 1.000000 -0.171225 0.108909 0.119437 0.078656 0.009817 -0.001536 -0.029530 0.055374 0.015230
%PTSFT -0.026550 -0.016905 0.086858 0.051201 0.050566 -0.290526 -0.110369 -0.084307 -0.246186 0.285242 0.276308 0.041051 0.056030 0.043063 0.049625 0.052775 0.117911 0.007439 0.054157 -0.032886 0.073973 0.109683 0.054935 0.037694 0.005583 0.026700 -0.011774 0.017924 -0.176749 -0.118304 0.059860 0.057776 0.048651 0.135623 -0.433099 -0.290967 0.176264 -0.000420 0.030655 0.005316 -0.083367 -0.090891 -0.054846 0.066598 -0.192410 -0.148595 -0.051532 -0.376576 -0.171225 1.000000 -0.129222 -0.126616 -0.259349 -0.096680 -0.328641 0.076533 -0.414645 -0.003624
%PTSOFFTO -0.116107 0.018578 -0.016638 -0.015458 -0.011706 0.044939 -0.002219 0.000845 0.039068 -0.020497 -0.019945 0.229101 -0.027428 -0.057218 -0.053086 -0.021240 -0.044408 0.139936 -0.034144 0.005814 -0.014394 -0.077705 -0.021254 -0.003015 0.022224 0.001298 0.016400 -0.023052 0.095988 0.022575 -0.023574 -0.075679 -0.066231 -0.058221 0.040327 0.047253 -0.105585 0.012979 -0.023429 0.002416 0.065297 0.044638 0.071585 0.058467 -0.022665 0.112691 0.043756 -0.038917 0.108909 -0.129222 1.000000 0.094287 0.127642 0.086077 0.101173 0.007002 0.019339 0.106465
%PTSPITP -0.137336 -0.047885 -0.039999 0.027996 -0.090487 0.590949 -0.491153 -0.484758 -0.408444 0.011176 0.075335 -0.151972 0.522477 0.233679 0.343391 -0.080517 0.047135 -0.060910 0.358421 0.198407 0.064932 0.220153 0.056841 -0.006536 0.017162 -0.022421 0.026968 -0.098144 -0.199121 -0.117218 0.635393 0.415706 0.580501 0.242068 0.284937 0.229186 -0.044664 0.064373 0.135928 -0.019952 0.047647 0.008259 0.078449 0.843660 -0.814764 0.938638 -0.252933 -0.813998 0.119437 -0.126616 0.094287 1.000000 0.247104 0.033092 -0.261742 -0.215453 -0.122006 0.251159
2FGM%AST 0.015655 -0.115571 -0.197412 -0.174075 -0.241023 0.374713 -0.174183 -0.201537 -0.020505 -0.226396 -0.202141 0.100670 0.247337 0.076586 0.137180 -0.425670 -0.302428 -0.260259 0.223246 0.097830 -0.172276 -0.036590 -0.079160 -0.031007 0.008063 0.031791 -0.013288 -0.531034 -0.206284 -0.375948 0.323206 0.243443 0.331210 -0.081048 0.392743 0.337876 -0.336992 0.049072 -0.018838 -0.065315 0.093275 0.090901 0.073001 0.093234 -0.052922 0.192745 -0.172408 -0.046794 0.078656 -0.259349 0.127642 0.247104 1.000000 -0.697542 0.236194 -0.486182 0.773596 -0.667663
2FGM%UAST 0.039718 0.305266 0.367293 0.355391 0.409555 -0.019165 0.295590 0.318662 0.107288 0.339564 0.323565 0.195130 -0.134427 0.074334 0.013162 0.523654 0.427283 0.324435 -0.124426 0.103337 0.340305 0.101178 0.101356 0.072220 0.118516 0.054166 0.059837 0.566061 0.278951 0.323669 -0.269522 -0.174812 -0.242546 0.037615 -0.048286 -0.010654 0.398588 -0.086627 0.179143 0.249614 0.152519 0.121253 0.148891 0.133680 -0.100613 0.139458 0.295634 -0.080777 0.009817 -0.096680 0.086077 0.033092 -0.697542 1.000000 -0.132585 0.551627 -0.743498 0.898825
3FGM%AST 0.020868 0.026122 -0.058219 -0.064089 -0.029832 -0.121650 0.113869 0.119421 0.584347 -0.120076 -0.155252 0.256770 -0.181373 -0.061567 -0.102779 -0.098820 -0.125464 -0.014121 -0.086044 0.047883 -0.084370 -0.148219 -0.039992 -0.021278 0.027437 0.045775 -0.006123 -0.081342 0.129007 0.041878 -0.258817 -0.122456 -0.195807 -0.208840 0.045743 0.059558 -0.136873 -0.067789 -0.067677 0.026623 0.119015 0.097203 0.113396 -0.342752 0.392324 -0.268679 0.001683 0.421201 -0.001536 -0.328641 0.101173 -0.261742 0.236194 -0.132585 1.000000 -0.288741 0.452273 -0.309824
3FGM%UAST 0.013203 0.356889 0.506853 0.472211 0.527010 -0.095382 0.463847 0.476755 0.241393 0.493395 0.469244 0.175276 -0.179885 0.115015 0.029368 0.576870 0.522398 0.346934 -0.107780 0.071721 0.436525 0.165092 0.156454 0.136110 0.120799 0.082255 0.044441 0.564587 0.241027 0.244618 -0.325879 -0.203483 -0.287006 0.000252 -0.044819 0.012918 0.528714 -0.118438 0.266234 0.287573 0.137737 0.148845 0.092042 -0.061382 0.073826 -0.145979 0.211830 0.097277 -0.029530 0.076533 0.007002 -0.215453 -0.486182 0.551627 -0.288741 1.000000 -0.562287 0.631530
FGM%AST 0.027992 -0.181382 -0.315100 -0.311867 -0.337194 0.138259 -0.079265 -0.109815 0.151911 -0.366770 -0.361292 0.062292 0.048466 -0.069850 -0.036760 -0.467892 -0.425212 -0.266962 0.068285 -0.023693 -0.300949 -0.164574 -0.127723 -0.055969 -0.063968 -0.014693 -0.041133 -0.515915 -0.118755 -0.234344 0.119056 0.076435 0.120907 -0.196610 0.303271 0.239762 -0.453046 0.030164 -0.148897 -0.144785 0.005317 0.017888 -0.009538 -0.282070 0.340071 -0.209775 -0.236185 0.410379 0.055374 -0.414645 0.019339 -0.122006 0.773596 -0.743498 0.452273 -0.562287 1.000000 -0.853034
FGM%UAST -0.012590 0.289378 0.406371 0.408323 0.426410 0.105023 0.150268 0.175289 -0.023200 0.426714 0.426745 0.088549 -0.006011 0.144197 0.106847 0.546260 0.500964 0.325863 -0.038397 0.125993 0.394651 0.199610 0.142270 0.065693 0.097334 0.029996 0.057901 0.597266 0.220256 0.301080 -0.109940 -0.070089 -0.098675 0.143277 -0.021534 0.019660 0.472688 -0.048140 0.259167 0.230703 0.105739 0.075885 0.112041 0.380810 -0.353513 0.364627 0.297817 -0.339708 0.015230 -0.003624 0.106465 0.251159 -0.667663 0.898825 -0.309824 0.631530 -0.853034 1.000000
In [8]:
# Lets now only see the correlations that meet certain thresholds. I set mine as 0.75. I also eliminate those that are the correlation of a column against itself

threshold = 0.75

positive_correlations = correlations[(correlations > threshold) & (correlations < 1)]
In [9]:
# Now we print the correlations and columns that have those correlations that meet the threshold

for column in positive_correlations:
    above_threshold = positive_correlations[column].dropna()
    for col, corr in above_threshold.iteritems():
        print(f"Correlation: {corr:.3f}, Columns: {column} and {col}")

Correlation: 0.874, Columns: Min and PTS
Correlation: 0.879, Columns: Min and FGM
Correlation: 0.884, Columns: Min and FGA
Correlation: 0.750, Columns: Min and DREB
Correlation: 0.787, Columns: Min and TOV
Correlation: 0.753, Columns: Min and PF
Correlation: 0.918, Columns: Min and FP
Correlation: 0.877, Columns: Min and POSS
Correlation: 0.874, Columns: PTS and Min
Correlation: 0.992, Columns: PTS and FGM
Correlation: 0.982, Columns: PTS and FGA
Correlation: 0.900, Columns: PTS and FTM
Correlation: 0.890, Columns: PTS and FTA
Correlation: 0.852, Columns: PTS and TOV
Correlation: 0.953, Columns: PTS and FP
Correlation: 0.768, Columns: PTS and POSS
Correlation: 0.879, Columns: FGM and Min
Correlation: 0.992, Columns: FGM and PTS
Correlation: 0.977, Columns: FGM and FGA
Correlation: 0.862, Columns: FGM and FTM
Correlation: 0.862, Columns: FGM and FTA
Correlation: 0.850, Columns: FGM and TOV
Correlation: 0.959, Columns: FGM and FP
Correlation: 0.770, Columns: FGM and POSS
Correlation: 0.884, Columns: FGA and Min
Correlation: 0.982, Columns: FGA and PTS
Correlation: 0.977, Columns: FGA and FGM
Correlation: 0.775, Columns: FGA and 3PA
Correlation: 0.842, Columns: FGA and FTM
Correlation: 0.829, Columns: FGA and FTA
Correlation: 0.849, Columns: FGA and TOV
Correlation: 0.931, Columns: FGA and FP
Correlation: 0.772, Columns: FGA and POSS
Correlation: 0.917, Columns: FG% and EFG%
Correlation: 0.874, Columns: FG% and TS%
Correlation: 0.982, Columns: 3PM and 3PA
Correlation: 0.775, Columns: 3PA and FGA
Correlation: 0.982, Columns: 3PA and 3PM
Correlation: 0.900, Columns: FTM and PTS
Correlation: 0.862, Columns: FTM and FGM
Correlation: 0.842, Columns: FTM and FGA
Correlation: 0.986, Columns: FTM and FTA
Correlation: 0.787, Columns: FTM and TOV
Correlation: 0.851, Columns: FTM and FP
Correlation: 0.890, Columns: FTA and PTS
Correlation: 0.862, Columns: FTA and FGM
Correlation: 0.829, Columns: FTA and FGA
Correlation: 0.986, Columns: FTA and FTM
Correlation: 0.790, Columns: FTA and TOV
Correlation: 0.857, Columns: FTA and FP
Correlation: 0.835, Columns: OREB and REB
Correlation: 0.750, Columns: DREB and Min
Correlation: 0.973, Columns: DREB and REB
Correlation: 0.837, Columns: DREB and FP
Correlation: 0.784, Columns: DREB and DD2
Correlation: 0.835, Columns: REB and OREB
Correlation: 0.973, Columns: REB and DREB
Correlation: 0.780, Columns: REB and FP
Correlation: 0.781, Columns: REB and DD2
Correlation: 0.832, Columns: AST and TOV
Correlation: 0.789, Columns: AST and FP
Correlation: 0.829, Columns: AST and AST%
Correlation: 0.787, Columns: TOV and Min
Correlation: 0.852, Columns: TOV and PTS
Correlation: 0.850, Columns: TOV and FGM
Correlation: 0.849, Columns: TOV and FGA
Correlation: 0.787, Columns: TOV and FTM
Correlation: 0.790, Columns: TOV and FTA
Correlation: 0.832, Columns: TOV and AST
Correlation: 0.869, Columns: TOV and FP
Correlation: 0.753, Columns: PF and Min
Correlation: 0.918, Columns: FP and Min
Correlation: 0.953, Columns: FP and PTS
Correlation: 0.959, Columns: FP and FGM
Correlation: 0.931, Columns: FP and FGA
Correlation: 0.851, Columns: FP and FTM
Correlation: 0.857, Columns: FP and FTA
Correlation: 0.837, Columns: FP and DREB
Correlation: 0.780, Columns: FP and REB
Correlation: 0.789, Columns: FP and AST
Correlation: 0.869, Columns: FP and TOV
Correlation: 0.796, Columns: FP and POSS
Correlation: 0.784, Columns: DD2 and DREB
Correlation: 0.781, Columns: DD2 and REB
Correlation: 0.796, Columns: OFFRTG and NETRTG
Correlation: 0.796, Columns: NETRTG and OFFRTG
Correlation: 0.829, Columns: AST% and AST
Correlation: 0.762, Columns: AST% and AST RATIO
Correlation: 0.762, Columns: AST RATIO and AST%
Correlation: 0.806, Columns: OREB% and REB%
Correlation: 0.919, Columns: DREB% and REB%
Correlation: 0.806, Columns: REB% and OREB%
Correlation: 0.919, Columns: REB% and DREB%
Correlation: 0.917, Columns: EFG% and FG%
Correlation: 0.954, Columns: EFG% and TS%
Correlation: 0.874, Columns: TS% and FG%
Correlation: 0.954, Columns: TS% and EFG%
Correlation: 0.877, Columns: POSS and Min
Correlation: 0.768, Columns: POSS and PTS
Correlation: 0.770, Columns: POSS and FGM
Correlation: 0.772, Columns: POSS and FGA
Correlation: 0.796, Columns: POSS and FP
Correlation: 0.881, Columns: POSS and GP
Correlation: 0.799, Columns: POSS and W
Correlation: 0.753, Columns: POSS and L
Correlation: 0.881, Columns: GP and POSS
Correlation: 0.891, Columns: GP and W
Correlation: 0.872, Columns: GP and L
Correlation: 0.799, Columns: W and POSS
Correlation: 0.891, Columns: W and GP
Correlation: 0.753, Columns: L and POSS
Correlation: 0.872, Columns: L and GP
Correlation: 0.906, Columns: %FGA2PT and %PTS2PT
Correlation: 0.844, Columns: %FGA2PT and %PTSPITP
Correlation: 0.916, Columns: %FGA3PT and %PTS3PT
Correlation: 0.906, Columns: %PTS2PT and %FGA2PT
Correlation: 0.939, Columns: %PTS2PT and %PTSPITP
Correlation: 0.916, Columns: %PTS3PT and %FGA3PT
Correlation: 0.844, Columns: %PTSPITP and %FGA2PT
Correlation: 0.939, Columns: %PTSPITP and %PTS2PT
Correlation: 0.774, Columns: 2FGM%AST and FGM%AST
Correlation: 0.899, Columns: 2FGM%UAST and FGM%UAST
Correlation: 0.774, Columns: FGM%AST and 2FGM%AST
Correlation: 0.899, Columns: FGM%UAST and 2FGM%UAST
In [10]:
# This one is for variables that are negatively correlated
threshold = -0.75

negative_correlations = correlations[correlations < threshold]

for column in negative_correlations:
    above_threshold = negative_correlations[column].dropna()
    for col, corr in above_threshold.iteritems():
        print(f"Correlation: {corr:.3f}, Columns: {column} and {col}")

Correlation: -0.962, Columns: %FGA2PT and %FGA3PT
Correlation: -0.883, Columns: %FGA2PT and %PTS3PT
Correlation: -0.962, Columns: %FGA3PT and %FGA2PT
Correlation: -0.872, Columns: %FGA3PT and %PTS2PT
Correlation: -0.815, Columns: %FGA3PT and %PTSPITP
Correlation: -0.872, Columns: %PTS2PT and %FGA3PT
Correlation: -0.860, Columns: %PTS2PT and %PTS3PT
Correlation: -0.883, Columns: %PTS3PT and %FGA2PT
Correlation: -0.860, Columns: %PTS3PT and %PTS2PT
Correlation: -0.814, Columns: %PTS3PT and %PTSPITP
Correlation: -0.815, Columns: %PTSPITP and %FGA3PT
Correlation: -0.814, Columns: %PTSPITP and %PTS3PT
Correlation: -0.853, Columns: FGM%AST and FGM%UAST
Correlation: -0.853, Columns: FGM%UAST and FGM%AST

There are many variables that are highly correlated that make sense. For example, FTM and FTA or REB and DREB. Knowing what we know about basketball, it makes sense that as the number of defensive rebounds go up, so do the number of total rebounds. In addition, the negative correlations make sense as well. For example, if you take more 2 point shots, then your percentage of 3 point shots will go down. There are many examples of this. These heavily correlated features will need to be taken care of, or we will need to use an algorithm that is not sensitive to high correlations

Visualizations¶

There are 60 columns in our dataframe, 58 of which are numeric. It's difficult to view all of those at the same time, so we will split them up into 3 sections so we can get a good look at histograms of all of them. I find it easier to look at the distibution using a KDE plot, so I have included those as well.

In [11]:
num_rows = 5
num_cols = 4

# Create subplots for histograms
fig, axes = plt.subplots(num_rows, num_cols, figsize=(15, 10))

# Generate histograms for all variables
for i, column in enumerate(df.columns[2:22]):
    ax = axes[i // num_cols, i % num_cols]  # Get the appropriate subplot
    ax.hist(df[column])
    ax.set_xlabel(column)
    ax.set_ylabel('Frequency')

# Adjust spacing between subplots
fig.tight_layout()

# Display the plot
plt.show()
In [12]:
num_rows = 5
num_cols = 4

# Create subplots for histograms
fig, axes = plt.subplots(num_rows, num_cols, figsize=(15, 10))

# Generate KDE plots for all variables
for i, column in enumerate(df.columns[2:22]):
    ax = axes[i // num_cols, i % num_cols]  # Get the appropriate subplot
    sns.kdeplot(data=df[column], ax=ax)
    ax.set_xlabel(column)
    ax.set_ylabel('Density')

# Adjust spacing between subplots
fig.tight_layout()

# Display the plot
plt.show()
In [13]:
num_rows = 5
num_cols = 4

# Create subplots for histograms
fig, axes = plt.subplots(num_rows, num_cols, figsize=(15, 10))

# Generate histograms for all variables
for i, column in enumerate(df.columns[22:42]):
    ax = axes[i // num_cols, i % num_cols]  # Get the appropriate subplot
    ax.hist(df[column])
    ax.set_xlabel(column)
    ax.set_ylabel('Frequency')


# Adjust spacing between subplots
fig.tight_layout()

# Display the plot
plt.show()
In [14]:
num_rows = 5
num_cols = 4

# Create subplots for histograms
fig, axes = plt.subplots(num_rows, num_cols, figsize=(15, 10))

# Generate KDE plots for all variables
for i, column in enumerate(df.columns[22:42]):
    ax = axes[i // num_cols, i % num_cols]  # Get the appropriate subplot
    sns.kdeplot(data=df[column], ax=ax)
    ax.set_xlabel(column)
    ax.set_ylabel('Density')


# Adjust spacing between subplots
fig.tight_layout()

# Display the plot
plt.show()
In [15]:
num_rows = 5
num_cols = 4

# Create subplots for histograms
fig, axes = plt.subplots(num_rows, num_cols, figsize=(15, 10))

# Generate histograms for all variables
for i, column in enumerate(df.columns[42:]):
    ax = axes[i // num_cols, i % num_cols]  # Get the appropriate subplot
    ax.hist(df[column])
    ax.set_xlabel(column)
    ax.set_ylabel('Frequency')

# Hide empty subplots
if i < num_rows * num_cols - 1:
    for j in range(i + 1, num_rows * num_cols):
        fig.delaxes(axes[j // num_cols, j % num_cols])

# Adjust spacing between subplots
fig.tight_layout()

# Display the plot
plt.show()
In [16]:
num_rows = 5
num_cols = 4

# Create subplots for histograms
fig, axes = plt.subplots(num_rows, num_cols, figsize=(15, 10))

# Generate KDE plots for all variables
for i, column in enumerate(df.columns[42:]):
    ax = axes[i // num_cols, i % num_cols]  # Get the appropriate subplot
    sns.kdeplot(data=df[column], ax=ax)
    ax.set_xlabel(column)
    ax.set_ylabel('Density')

# Hide empty subplots
if i < num_rows * num_cols - 1:
    for j in range(i + 1, num_rows * num_cols):
        fig.delaxes(axes[j // num_cols, j % num_cols])

# Adjust spacing between subplots
fig.tight_layout()

# Display the plot
plt.show()
In [17]:
# If you want a closer look at each histogram, you can run this code. It will be commented out for now since there are many graphs

#for column in df.columns[2:]:
 #   plt.hist(df[column])
  #  plt.xlabel(column)
   # plt.ylabel('Frequency')
    #plt.show()

There are a number of things we can see from these graphs. Many of the offensive statistics are positively skewed. This makes sense given that there are rather few players that would have large amounts of points, rebounds, assists, etc. in a game. These players would be considered superstars, and there aren't that many in the league. There are also several variables that are not skewed or at least close to normal. These include DEFRTG, NETRTG, EFG%, TS%, PIE and PACE. There are other variables that are oddly distributed, such as W, POSS and Min.

In [ ]:

Clustering¶

The main point of my project is to try to cluster the different players in the NBA based on their statistics from this past year. That involves some sort of clustering. I will try to just run the clusters and look at the labels of each, and later I will use dimension reduction to be able to visualize the clusters a little better.

In [18]:
df.head()
Out[18]:
Player Team Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST
0 Joel Embiid PHI 29 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4 119.0 110.2 8.8 23.3 1.21 12.7 5.7 24.3 15.7 10.5 57.3 65.5 37.0 97.34 21.3 4639 66 43 23 84.9 15.1 60.7 15.7 9.1 6.3 30.2 12.7 45.0 60.0 40.0 89.4 10.6 62.6 37.4
1 Luka Doncic DAL 24 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9 118.1 116.0 2.1 40.8 2.24 21.1 2.4 22.4 12.4 9.4 56.0 60.9 36.8 97.63 20.2 4874 66 33 33 62.7 37.3 50.0 8.5 26.0 5.2 24.0 14.0 41.4 13.1 86.9 21.6 78.4 15.3 84.7
2 Damian Lillard POR 32 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8 119.5 117.4 2.1 33.8 2.23 20.8 2.2 11.2 6.8 9.3 56.4 64.5 33.1 99.78 17.3 4385 58 27 31 45.3 54.7 33.4 6.0 39.2 8.6 27.4 11.9 27.4 15.7 84.3 51.6 48.4 31.5 68.5
3 Shai Gilgeous-Alexander OKC 24 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2 116.1 113.3 2.7 24.9 1.93 16.4 2.3 10.9 6.5 8.5 53.1 62.6 31.8 103.47 17.5 5211 68 33 35 87.8 12.2 60.5 9.7 8.1 12.7 31.4 17.7 50.8 20.1 79.9 31.0 69.0 21.0 79.0
4 Giannis Antetokounmpo MIL 28 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4 116.4 109.2 7.2 31.4 1.46 16.2 6.5 26.8 17.1 11.1 57.2 60.5 37.3 103.63 20.4 4380 63 47 16 86.6 13.4 67.4 7.0 7.2 17.5 25.4 12.9 60.3 41.5 58.5 61.7 38.3 42.9 57.1
In [19]:
#We need to drop all non-numeric columns. We will drop Player and Team.

df1 = df.drop(['Player', 'Team'], axis=1)
In [20]:
df1.head()
Out[20]:
Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST
0 29 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4 119.0 110.2 8.8 23.3 1.21 12.7 5.7 24.3 15.7 10.5 57.3 65.5 37.0 97.34 21.3 4639 66 43 23 84.9 15.1 60.7 15.7 9.1 6.3 30.2 12.7 45.0 60.0 40.0 89.4 10.6 62.6 37.4
1 24 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9 118.1 116.0 2.1 40.8 2.24 21.1 2.4 22.4 12.4 9.4 56.0 60.9 36.8 97.63 20.2 4874 66 33 33 62.7 37.3 50.0 8.5 26.0 5.2 24.0 14.0 41.4 13.1 86.9 21.6 78.4 15.3 84.7
2 32 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8 119.5 117.4 2.1 33.8 2.23 20.8 2.2 11.2 6.8 9.3 56.4 64.5 33.1 99.78 17.3 4385 58 27 31 45.3 54.7 33.4 6.0 39.2 8.6 27.4 11.9 27.4 15.7 84.3 51.6 48.4 31.5 68.5
3 24 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2 116.1 113.3 2.7 24.9 1.93 16.4 2.3 10.9 6.5 8.5 53.1 62.6 31.8 103.47 17.5 5211 68 33 35 87.8 12.2 60.5 9.7 8.1 12.7 31.4 17.7 50.8 20.1 79.9 31.0 69.0 21.0 79.0
4 28 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4 116.4 109.2 7.2 31.4 1.46 16.2 6.5 26.8 17.1 11.1 57.2 60.5 37.3 103.63 20.4 4380 63 47 16 86.6 13.4 67.4 7.0 7.2 17.5 25.4 12.9 60.3 41.5 58.5 61.7 38.3 42.9 57.1
In [21]:
# Next we need to standardize the data since clustering is sensitive to scale. I will use standard scaler

scaler = StandardScaler()
X = scaler.fit_transform(df1)

The common way of determining the correct number of clusters for kmeans clustering is the elbow method. However, the elbow method may not always be the most accurate, particularly when the number of clusters is high. The Calinski-Harabasz score, Davies-Bouldin score and the Silhouette score can all give a more accurate number of clusters. I will run each of the four methods here, and I will compare. Check out the Sklearn notes for each of these and other methods under clustering metrics: https://scikit-learn.org/stable/modules/classes.html#module-sklearn.metrics

In addition, check out this blog post: https://towardsdatascience.com/are-you-still-using-the-elbow-method-5d271b3063bd This was one of the main reasons I chose the metrics I used. Because we don't have the true labels, many of the other clustering metrics don't work. That's why I chose the three scores given above

In [22]:
wcss = []
ch_scores = []
db_scores = []
s_scores = []

for i in range(2, 25):
    kmeans = KMeans(n_clusters=i, init='k-means++', random_state = 9)
    kmeans.fit(X)
    wcss.append(kmeans.inertia_)
    ch_scores.append(calinski_harabasz_score(X, kmeans.labels_))
    db_scores.append(davies_bouldin_score(X, kmeans.labels_))
    s_scores.append(silhouette_score(X, kmeans.labels_))
In [23]:
fig, ax = plt.subplots(2,2, figsize=(12,12))

ax[0,0].plot(range(2, 25), wcss)
ax[0,0].set_title('K Means with Elbow Method (Lowest)')
ax[0,0].set_xticks(range(2,25))
ax[0,1].plot(range(2, 25), ch_scores)
ax[0,1].set_title('K Means with Calinski-Harabasz Method (Highest)')
ax[0,1].set_xticks(range(2,25))
ax[1,0].plot(range(2, 25), s_scores)
ax[1,0].set_title('K Means with Silhouette Method (Highest)')
ax[1,0].set_xticks(range(2,25))
ax[1,1].plot(range(2, 25), db_scores)
ax[1,1].set_title('K Means with Davies-Boulding Method (Lowest)')
ax[1,1].set_xticks(range(2,25))

fig.show()

C:\Users\tfurr\AppData\Local\Temp\ipykernel_4064\2825464523.py:16: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.
  fig.show()

The four methods don't come to a concensus on the correct number of clusters, though they don't necessarily need to. The thing that concerns me is that none of them are even close. The elbow method is smooth and curved, with no distinct "elbow". The same can be said for the Calinski-Harabasz method. The silhouette method recommends anything from 2 to 5 and maybe 10. The Davies-Boulding method recommends 16 or 20. I suspect there are issues here that we can address, so I'm not even going to perform the clustering here. We already know there are variables that are highly correlated. So I will perform PCA and later on I will also filter the data.

Using PCA and clustering¶

In [24]:
pca1 = PCA(n_components=25)
X_pca1 = pca1.fit_transform(X)
In [25]:
plt.bar(range(1, 21), pca1.explained_variance_ratio_[0:20])
plt.xlabel('Principal Component')
plt.ylabel('Explained Variance Ratio')
plt.xticks(np.arange(1, 21))
plt.show()
In [26]:
pca1.explained_variance_ratio_
Out[26]:
array([0.27536352, 0.15784169, 0.09534806, 0.05414205, 0.04786986,
       0.04062998, 0.03685692, 0.02583204, 0.02390873, 0.02093006,
       0.02021895, 0.01858952, 0.01674272, 0.01608989, 0.01456463,
       0.01396763, 0.01317754, 0.01155616, 0.01024437, 0.00932619,
       0.00839855, 0.0079888 , 0.00736582, 0.00689754, 0.00620988])

The first 3 components explain almost 53% of the variation in the data so I will just use those 3. You could make an argument for other numbers as well such as 2 or 4. I feel comfortable with the first 3.

In [27]:
pca = PCA(n_components=3)
X_pca = pca.fit_transform(X)
In [28]:
# This is the same as above. I get the 4 scores and plot them for this new PCA data

wcss = []
ch_scores = []
db_scores = []
s_scores = []

for i in range(2, 25):
    kmeans = KMeans(n_clusters=i, init='k-means++', random_state = 9)
    kmeans.fit(X_pca)
    wcss.append(kmeans.inertia_)
    ch_scores.append(calinski_harabasz_score(X_pca, kmeans.labels_))
    db_scores.append(davies_bouldin_score(X_pca, kmeans.labels_))
    s_scores.append(silhouette_score(X_pca, kmeans.labels_))
In [29]:
fig, ax = plt.subplots(2,2, figsize=(12,12))

ax[0,0].plot(range(2, 25), wcss)
ax[0,0].set_title('K Means with Elbow Method (Lowest)')
ax[0,0].set_xticks(range(2,25))
ax[0,1].plot(range(2, 25), ch_scores)
ax[0,1].set_title('K Means with Calinski-Harabasz Method (Highest)')
ax[0,1].set_xticks(range(2,25))
ax[1,0].plot(range(2, 25), s_scores)
ax[1,0].set_title('K Means with Silhouette Method (Highest)')
ax[1,0].set_xticks(range(2,25))
ax[1,1].plot(range(2, 25), db_scores)
ax[1,1].set_title('K Means with Davies-Boulding Method (Lowest)')
ax[1,1].set_xticks(range(2,25))

fig.show()

C:\Users\tfurr\AppData\Local\Temp\ipykernel_4064\2825464523.py:16: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.
  fig.show()

Performing PCA has given a more concrete answer to the number of clusters. The elbow method might give about 6, though it's still pretty smooth. However, the other 3 methods all have definitive spikes in their respective directions at 6. In addition, the bottom two methods both have distinctive spikes at 17. I will look at the clustering with both 6 and 17 clusters.

In [30]:
kmeans = KMeans(n_clusters=6)
kmeans.fit(X_pca)

labels6 = kmeans.labels_

df['labels_6'] = labels6

kmeans2 = KMeans(n_clusters=17)
kmeans2.fit(X_pca)

labels17 = kmeans2.labels_

df['labels_17'] = labels17
In [31]:
# Make sure it looks correct
df.head()
Out[31]:
Player Team Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST labels_6 labels_17
0 Joel Embiid PHI 29 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4 119.0 110.2 8.8 23.3 1.21 12.7 5.7 24.3 15.7 10.5 57.3 65.5 37.0 97.34 21.3 4639 66 43 23 84.9 15.1 60.7 15.7 9.1 6.3 30.2 12.7 45.0 60.0 40.0 89.4 10.6 62.6 37.4 4 13
1 Luka Doncic DAL 24 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9 118.1 116.0 2.1 40.8 2.24 21.1 2.4 22.4 12.4 9.4 56.0 60.9 36.8 97.63 20.2 4874 66 33 33 62.7 37.3 50.0 8.5 26.0 5.2 24.0 14.0 41.4 13.1 86.9 21.6 78.4 15.3 84.7 4 1
2 Damian Lillard POR 32 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8 119.5 117.4 2.1 33.8 2.23 20.8 2.2 11.2 6.8 9.3 56.4 64.5 33.1 99.78 17.3 4385 58 27 31 45.3 54.7 33.4 6.0 39.2 8.6 27.4 11.9 27.4 15.7 84.3 51.6 48.4 31.5 68.5 4 1
3 Shai Gilgeous-Alexander OKC 24 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2 116.1 113.3 2.7 24.9 1.93 16.4 2.3 10.9 6.5 8.5 53.1 62.6 31.8 103.47 17.5 5211 68 33 35 87.8 12.2 60.5 9.7 8.1 12.7 31.4 17.7 50.8 20.1 79.9 31.0 69.0 21.0 79.0 4 1
4 Giannis Antetokounmpo MIL 28 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4 116.4 109.2 7.2 31.4 1.46 16.2 6.5 26.8 17.1 11.1 57.2 60.5 37.3 103.63 20.4 4380 63 47 16 86.6 13.4 67.4 7.0 7.2 17.5 25.4 12.9 60.3 41.5 58.5 61.7 38.3 42.9 57.1 4 13
In [32]:
df['labels_6'].value_counts() # See how many are in each
Out[32]:
2    141
0    124
1     84
3     71
5     61
4     58
Name: labels_6, dtype: int64
In [33]:
df['labels_17'].value_counts() # See how many are in each
Out[33]:
0     50
7     49
4     49
6     40
16    38
5     37
12    37
9     35
11    35
3     35
1     33
14    30
2     21
15    18
10    15
13    11
8      6
Name: labels_17, dtype: int64
In [34]:
df.loc[df['labels_6'] == 1, 'Player'] # Look at some of the players.
Out[34]:
160        Jeenathan Williams
199            Hamidou Diallo
208             Jae'Sean Tate
237        Aleksej Pokusevski
253               T.J. Warren
                ...          
512    Thanasis Antetokounmpo
514               Braxton Key
516             Tyrese Martin
522               Noah Vonleh
523              Chima Moneke
Name: Player, Length: 84, dtype: object
In [35]:
# This creates a new dataframe that we will use for the visualizations. Includes the player names, the PCA components and the cluster labels for 6 and 17
df_new = pd.DataFrame({'Player': df.Player, 'PC1': X_pca[:, 0], 'PC2': X_pca[:, 1], 'PC3': X_pca[:, 2], 'Cluster6': df.labels_6, 'Cluster17':df.labels_17})
In [36]:
# Make sure the cluster labels are categorical 
df_new['Cluster6'] = df_new['Cluster6'].astype('category')
df_new['Cluster17'] = df_new['Cluster17'].astype('category')
In [37]:
fig = px.scatter(df_new, x='PC1', y='PC2', color='Cluster6', hover_data=['Player'],
                 title="2023 NBA Regular Season Stats Clustering with 6 clusters on 2 Components")

fig.show()
In [38]:
fig = px.scatter(df_new, x='PC1', y='PC2', color='Cluster17', hover_data=['Player'],
                 title="2023 NBA Regular Season Stats Clustering with 17 clusters on 2 Components",
                color_discrete_sequence=px.colors.qualitative.Alphabet)

fig.show()

I did include all 3 components in the data, so we may as well look at the 3d version

In [39]:
fig = px.scatter_3d(df_new, x='PC1', y='PC2',z='PC3', color='Cluster6', hover_data=['Player'],
                 title="2023 NBA Regular Season Stats Clustering with 6 clusters on 3 Components")

fig.show()
In [40]:
fig = px.scatter_3d(df_new, x='PC1', y='PC2', z='PC3', color='Cluster17', hover_data=['Player'],
                    title="2023 NBA Regular Season Stats Clustering with 17 clusters on 3 Components",
                    color_discrete_sequence=px.colors.qualitative.Alphabet)

fig.show()

All 4 of these graphs show interesting trends amongst the data. I am not attempting to label any of these clusters, though we could do that. I won't pretend I know enough about the intricate nature of basketball or all the players that played this year. However, I can tell that in the graphs with 6 clusters, cluster 2 would probably be considered high rebounding, traditional big men, cluster 5 would be "superstars" clusters 0 and 3 would probably be more "role players" and clusters 1 and 4 would likely be players that don't play as much. With the 17 clusters it's much more difficult for me to define. However, it's interesting to look at who is in each cluster.

Running clustering with filtered data¶

One of the issues I can see is that there a number of players who don't play much. I said before I would filter out these players, but I wanted to see what the clusters would look like with those players in the data set. I will now filter out those players.

In [41]:
df.head()
Out[41]:
Player Team Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST labels_6 labels_17
0 Joel Embiid PHI 29 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4 119.0 110.2 8.8 23.3 1.21 12.7 5.7 24.3 15.7 10.5 57.3 65.5 37.0 97.34 21.3 4639 66 43 23 84.9 15.1 60.7 15.7 9.1 6.3 30.2 12.7 45.0 60.0 40.0 89.4 10.6 62.6 37.4 4 13
1 Luka Doncic DAL 24 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9 118.1 116.0 2.1 40.8 2.24 21.1 2.4 22.4 12.4 9.4 56.0 60.9 36.8 97.63 20.2 4874 66 33 33 62.7 37.3 50.0 8.5 26.0 5.2 24.0 14.0 41.4 13.1 86.9 21.6 78.4 15.3 84.7 4 1
2 Damian Lillard POR 32 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8 119.5 117.4 2.1 33.8 2.23 20.8 2.2 11.2 6.8 9.3 56.4 64.5 33.1 99.78 17.3 4385 58 27 31 45.3 54.7 33.4 6.0 39.2 8.6 27.4 11.9 27.4 15.7 84.3 51.6 48.4 31.5 68.5 4 1
3 Shai Gilgeous-Alexander OKC 24 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2 116.1 113.3 2.7 24.9 1.93 16.4 2.3 10.9 6.5 8.5 53.1 62.6 31.8 103.47 17.5 5211 68 33 35 87.8 12.2 60.5 9.7 8.1 12.7 31.4 17.7 50.8 20.1 79.9 31.0 69.0 21.0 79.0 4 1
4 Giannis Antetokounmpo MIL 28 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4 116.4 109.2 7.2 31.4 1.46 16.2 6.5 26.8 17.1 11.1 57.2 60.5 37.3 103.63 20.4 4380 63 47 16 86.6 13.4 67.4 7.0 7.2 17.5 25.4 12.9 60.3 41.5 58.5 61.7 38.3 42.9 57.1 4 13

There's a definitive problem in figuring out where the threshold is for players to be kept in the dataset. I landed on 21 games played and 8 minutes per game. In this sense, the player must have played over a quarter of the games of the NBA season and played at least a sixth of the minutes per game. You could certainly make the case for other numbers as well. I felt this was a reasonable amount that would eliminate garbage time players and players that were injured for most of the season.

In [42]:
filtered_df = df[(df['GP'] > 21) & (df['Min'] > 8)].copy()
filtered_df1 = filtered_df.drop(['Player', 'Team', 'labels_6', 'labels_17'], axis=1)
In [43]:
filtered_df1.head() # Take a look
Out[43]:
Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST
0 29 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4 119.0 110.2 8.8 23.3 1.21 12.7 5.7 24.3 15.7 10.5 57.3 65.5 37.0 97.34 21.3 4639 66 43 23 84.9 15.1 60.7 15.7 9.1 6.3 30.2 12.7 45.0 60.0 40.0 89.4 10.6 62.6 37.4
1 24 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9 118.1 116.0 2.1 40.8 2.24 21.1 2.4 22.4 12.4 9.4 56.0 60.9 36.8 97.63 20.2 4874 66 33 33 62.7 37.3 50.0 8.5 26.0 5.2 24.0 14.0 41.4 13.1 86.9 21.6 78.4 15.3 84.7
2 32 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8 119.5 117.4 2.1 33.8 2.23 20.8 2.2 11.2 6.8 9.3 56.4 64.5 33.1 99.78 17.3 4385 58 27 31 45.3 54.7 33.4 6.0 39.2 8.6 27.4 11.9 27.4 15.7 84.3 51.6 48.4 31.5 68.5
3 24 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2 116.1 113.3 2.7 24.9 1.93 16.4 2.3 10.9 6.5 8.5 53.1 62.6 31.8 103.47 17.5 5211 68 33 35 87.8 12.2 60.5 9.7 8.1 12.7 31.4 17.7 50.8 20.1 79.9 31.0 69.0 21.0 79.0
4 28 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4 116.4 109.2 7.2 31.4 1.46 16.2 6.5 26.8 17.1 11.1 57.2 60.5 37.3 103.63 20.4 4380 63 47 16 86.6 13.4 67.4 7.0 7.2 17.5 25.4 12.9 60.3 41.5 58.5 61.7 38.3 42.9 57.1
In [44]:
filtered_df1.info() # Make sure we have 416 players

<class 'pandas.core.frame.DataFrame'>
Int64Index: 416 entries, 0 to 481
Data columns (total 58 columns):
 #   Column      Non-Null Count  Dtype  
---  ------      --------------  -----  
 0   Age         416 non-null    int64  
 1   Min         416 non-null    float64
 2   PTS         416 non-null    float64
 3   FGM         416 non-null    float64
 4   FGA         416 non-null    float64
 5   FG%         416 non-null    float64
 6   3PM         416 non-null    float64
 7   3PA         416 non-null    float64
 8   3P%         416 non-null    float64
 9   FTM         416 non-null    float64
 10  FTA         416 non-null    float64
 11  FT%         416 non-null    float64
 12  OREB        416 non-null    float64
 13  DREB        416 non-null    float64
 14  REB         416 non-null    float64
 15  AST         416 non-null    float64
 16  TOV         416 non-null    float64
 17  STL         416 non-null    float64
 18  BLK         416 non-null    float64
 19  PF          416 non-null    float64
 20  FP          416 non-null    float64
 21  DD2         416 non-null    float64
 22  TD3         416 non-null    float64
 23  +/-         416 non-null    float64
 24  OFFRTG      416 non-null    float64
 25  DEFRTG      416 non-null    float64
 26  NETRTG      416 non-null    float64
 27  AST%        416 non-null    float64
 28  AST/TO      416 non-null    float64
 29  AST RATIO   416 non-null    float64
 30  OREB%       416 non-null    float64
 31  DREB%       416 non-null    float64
 32  REB%        416 non-null    float64
 33  TO RATIO    416 non-null    float64
 34  EFG%        416 non-null    float64
 35  TS%         416 non-null    float64
 36  USG%        416 non-null    float64
 37  PACE        416 non-null    float64
 38  PIE         416 non-null    float64
 39  POSS        416 non-null    int64  
 40  GP          416 non-null    int64  
 41  W           416 non-null    int64  
 42  L           416 non-null    int64  
 43  %FGA2PT     416 non-null    float64
 44  %FGA3PT     416 non-null    float64
 45  %PTS2PT     416 non-null    float64
 46  %PTS2PT MR  416 non-null    float64
 47  %PTS3PT     416 non-null    float64
 48  %PTSFBPs    416 non-null    float64
 49  %PTSFT      416 non-null    float64
 50  %PTSOFFTO   416 non-null    float64
 51  %PTSPITP    416 non-null    float64
 52  2FGM%AST    416 non-null    float64
 53  2FGM%UAST   416 non-null    float64
 54  3FGM%AST    416 non-null    float64
 55  3FGM%UAST   416 non-null    float64
 56  FGM%AST     416 non-null    float64
 57  FGM%UAST    416 non-null    float64
dtypes: float64(53), int64(5)
memory usage: 191.8 KB

We will do the same scaling, as well as scoring and visualizations to determine how many clusters we should include

In [45]:
scaler = StandardScaler()
filtered_X = scaler.fit_transform(filtered_df1)
In [46]:
wcss = []
ch_scores = []
db_scores = []
s_scores = []

for i in range(2, 25):
    kmeans = KMeans(n_clusters=i, init='k-means++', random_state = 9)
    kmeans.fit(filtered_X)
    wcss.append(kmeans.inertia_)
    ch_scores.append(calinski_harabasz_score(filtered_X, kmeans.labels_))
    db_scores.append(davies_bouldin_score(filtered_X, kmeans.labels_))
    s_scores.append(silhouette_score(filtered_X, kmeans.labels_))
In [47]:
fig, ax = plt.subplots(2,2, figsize=(12,12))

ax[0,0].plot(range(2, 25), wcss)
ax[0,0].set_title('K Means with Elbow Method (Lowest)')
ax[0,0].set_xticks(range(2,25))
ax[0,1].plot(range(2, 25), ch_scores)
ax[0,1].set_title('K Means with Calinski-Harabasz Method (Highest)')
ax[0,1].set_xticks(range(2,25))
ax[1,0].plot(range(2, 25), s_scores)
ax[1,0].set_title('K Means with Silhouette Method (Highest)')
ax[1,0].set_xticks(range(2,25))
ax[1,1].plot(range(2, 25), db_scores)
ax[1,1].set_title('K Means with Davies-Boulding Method (Lowest)')
ax[1,1].set_xticks(range(2,25))

fig.show()

C:\Users\tfurr\AppData\Local\Temp\ipykernel_4064\2825464523.py:16: UserWarning:

Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.

This is really encouraging. By filtering out the players that don't play much, the elbow method has a little more of an elbow at 3 (though it's still pretty smooth), and the other 3 methods all point to 3 clusters. While the Davies-Boulding method suggests 15 or 18 as well, I will stick with 3

In [48]:
kmeans = KMeans(n_clusters=3)
kmeans.fit(filtered_X)

labels3 = kmeans.labels_ # Save the labels

# Use this line to make sure a warning does not appear as a copy of a slice
filtered_df.loc[:, 'labels_3'] = labels3
In [49]:
filtered_df['labels_3'] = filtered_df['labels_3'].astype('category') # make sure these are categorical

Let's look at some of the players in each of the clusters

In [50]:
filtered_df.loc[filtered_df['labels_3'] == 1, 'Player']
Out[50]:
16         Anthony Davis
50           Bam Adebayo
64     Jaren Jackson Jr.
67         Deandre Ayton
68          Myles Turner
             ...        
448     Christian Koloko
451       Richaun Holmes
453          Robin Lopez
459         Usman Garuba
469       Moussa Diabate
Name: Player, Length: 92, dtype: object
In [51]:
filtered_df.loc[filtered_df['labels_3'] == 0, 'Player']
Out[51]:
71     Michael Porter Jr.
74         Andrew Wiggins
87        P.J. Washington
88        Cameron Johnson
89        De'Andre Hunter
              ...        
468       Kessler Edwards
473             Ish Smith
476       Jeff Dowtin Jr.
478           Theo Pinson
481         Trent Forrest
Name: Player, Length: 216, dtype: object
In [52]:
filtered_df.loc[filtered_df['labels_3'] == 2, 'Player']
Out[52]:
0                  Joel Embiid
1                  Luka Doncic
2               Damian Lillard
3      Shai Gilgeous-Alexander
4        Giannis Antetokounmpo
                ...           
166              Cameron Payne
167               Monte Morris
185                  Josh Hart
197              Kyle Anderson
224             T.J. McConnell
Name: Player, Length: 108, dtype: object
In [53]:
filtered_df.head() # Take a look
Out[53]:
Player Team Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST labels_6 labels_17 labels_3
0 Joel Embiid PHI 29 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4 119.0 110.2 8.8 23.3 1.21 12.7 5.7 24.3 15.7 10.5 57.3 65.5 37.0 97.34 21.3 4639 66 43 23 84.9 15.1 60.7 15.7 9.1 6.3 30.2 12.7 45.0 60.0 40.0 89.4 10.6 62.6 37.4 4 13 2
1 Luka Doncic DAL 24 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9 118.1 116.0 2.1 40.8 2.24 21.1 2.4 22.4 12.4 9.4 56.0 60.9 36.8 97.63 20.2 4874 66 33 33 62.7 37.3 50.0 8.5 26.0 5.2 24.0 14.0 41.4 13.1 86.9 21.6 78.4 15.3 84.7 4 1 2
2 Damian Lillard POR 32 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8 119.5 117.4 2.1 33.8 2.23 20.8 2.2 11.2 6.8 9.3 56.4 64.5 33.1 99.78 17.3 4385 58 27 31 45.3 54.7 33.4 6.0 39.2 8.6 27.4 11.9 27.4 15.7 84.3 51.6 48.4 31.5 68.5 4 1 2
3 Shai Gilgeous-Alexander OKC 24 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2 116.1 113.3 2.7 24.9 1.93 16.4 2.3 10.9 6.5 8.5 53.1 62.6 31.8 103.47 17.5 5211 68 33 35 87.8 12.2 60.5 9.7 8.1 12.7 31.4 17.7 50.8 20.1 79.9 31.0 69.0 21.0 79.0 4 1 2
4 Giannis Antetokounmpo MIL 28 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4 116.4 109.2 7.2 31.4 1.46 16.2 6.5 26.8 17.1 11.1 57.2 60.5 37.3 103.63 20.4 4380 63 47 16 86.6 13.4 67.4 7.0 7.2 17.5 25.4 12.9 60.3 41.5 58.5 61.7 38.3 42.9 57.1 4 13 2

When I don't have dimension reduction, it's a little more difficult to get a good visualization. There are so many columns to look at that with 2 or even 3 dimensions we are not likely to see definitive splits. That being said, it's interesting to see. We can change the variables as well to look at different combinations of variables.

In [54]:
fig = px.scatter(filtered_df, x='NETRTG', y='PIE', color='labels_3', hover_data=['Player'],
                 title="2023 NBA Regular Filtered Season Stats Clustering on 2 Variables")

fig.show()
In [55]:
fig = px.scatter_3d(filtered_df, x='NETRTG', y='PIE', z='TS%', color='labels_3', hover_data=['Player'],
                 title="2023 NBA Regular Filtered Season Stats Clustering on 3 Variables")

fig.show()

In this case, I honestly don't have any definitive labels for these clusters. The only thing I can see is that many of the players in cluster 2 are big men that generally have a lot of rebounds. Other than that, I'm not entirely sure.

Using PCA and clustering on the filtered data¶

Like before, I will look at PCA for this filtered data

In [56]:
filtered_pca1 = PCA(n_components = 25)
filtered_X_pca1 = filtered_pca1.fit_transform(filtered_X)
In [57]:
plt.bar(range(1, 21), filtered_pca1.explained_variance_ratio_[0:20])
plt.xlabel('Principal Component')
plt.ylabel('Explained Variance Ratio')
plt.xticks(np.arange(1, 21))
plt.show()
In [58]:
filtered_pca1.explained_variance_ratio_
Out[58]:
array([0.28123134, 0.20948999, 0.10193812, 0.05984639, 0.04173367,
       0.03754766, 0.03023536, 0.02516983, 0.02184808, 0.01966989,
       0.01890735, 0.01838053, 0.01550588, 0.01466067, 0.01327966,
       0.00997892, 0.00980196, 0.00864983, 0.00741003, 0.00727333,
       0.00648518, 0.00592371, 0.00530741, 0.00510965, 0.00427241])

The first 4 components explain about 65% of the variance in the filtered data. So I am going to keep those components. An argument could have been made to just keep the first 2 considering they explain 48% of the variance. I felt 4 components was an appropriate amount

This is the same as before, I run PCA, get the scores and plot them to find the correct number of clusters

In [59]:
filtered_pca = PCA(n_components = 4)
filtered_X_pca = filtered_pca.fit_transform(filtered_X)
In [60]:
wcss = []
ch_scores = []
db_scores = []
s_scores = []

for i in range(2, 25):
    kmeans = KMeans(n_clusters=i, init='k-means++', random_state = 9)
    kmeans.fit(filtered_X_pca)
    wcss.append(kmeans.inertia_)
    ch_scores.append(calinski_harabasz_score(filtered_X_pca, kmeans.labels_))
    db_scores.append(davies_bouldin_score(filtered_X_pca, kmeans.labels_))
    s_scores.append(silhouette_score(filtered_X_pca, kmeans.labels_))
In [61]:
fig, ax = plt.subplots(2,2, figsize=(12,12))

ax[0,0].plot(range(2, 25), wcss)
ax[0,0].set_title('K Means with Elbow Method (Lowest)')
ax[0,0].set_xticks(range(2,25))
ax[0,1].plot(range(2, 25), ch_scores)
ax[0,1].set_title('K Means with Calinski-Harabasz Method (Highest)')
ax[0,1].set_xticks(range(2,25))
ax[1,0].plot(range(2, 25), s_scores)
ax[1,0].set_title('K Means with Silhouette Method (Highest)')
ax[1,0].set_xticks(range(2,25))
ax[1,1].plot(range(2, 25), db_scores)
ax[1,1].set_title('K Means with Davies-Boulding Method (Lowest)')
ax[1,1].set_xticks(range(2,25))

fig.show()

C:\Users\tfurr\AppData\Local\Temp\ipykernel_4064\2825464523.py:16: UserWarning:

Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.

We can see from our graphs above that the silhouette, Davies-Boulding and Calinski-Harabasz scores all give 3 clusters as the best number of clusters, just like with the original filtered data. We will perform k-means with 3 clusters and see the results.

In [62]:
kmeans = KMeans(n_clusters=3)
kmeans.fit(filtered_X_pca)

labels3_pca = kmeans.labels_

# Use this line to make sure a warning does not appear as a copy of a slice
filtered_df.loc[:, 'labels_3_pca'] = labels3_pca
In [63]:
filtered_df.head()
Out[63]:
Player Team Age Min PTS FGM FGA FG% 3PM 3PA 3P% FTM FTA FT% OREB DREB REB AST TOV STL BLK PF FP DD2 TD3 +/- OFFRTG DEFRTG NETRTG AST% AST/TO AST RATIO OREB% DREB% REB% TO RATIO EFG% TS% USG% PACE PIE POSS GP W L %FGA2PT %FGA3PT %PTS2PT %PTS2PT MR %PTS3PT %PTSFBPs %PTSFT %PTSOFFTO %PTSPITP 2FGM%AST 2FGM%UAST 3FGM%AST 3FGM%UAST FGM%AST FGM%UAST labels_6 labels_17 labels_3 labels_3_pca
0 Joel Embiid PHI 29 34.6 33.1 11.0 20.1 54.8 1.0 3.0 33.0 10.0 11.7 85.7 1.7 8.4 10.2 4.2 3.4 1.0 1.7 3.1 56.2 39.0 1.0 6.4 119.0 110.2 8.8 23.3 1.21 12.7 5.7 24.3 15.7 10.5 57.3 65.5 37.0 97.34 21.3 4639 66 43 23 84.9 15.1 60.7 15.7 9.1 6.3 30.2 12.7 45.0 60.0 40.0 89.4 10.6 62.6 37.4 4 13 2 0
1 Luka Doncic DAL 24 36.2 32.4 10.9 22.0 49.6 2.8 8.2 34.2 7.8 10.5 74.2 0.8 7.8 8.6 8.0 3.6 1.4 0.5 2.5 56.8 36.0 10.0 1.9 118.1 116.0 2.1 40.8 2.24 21.1 2.4 22.4 12.4 9.4 56.0 60.9 36.8 97.63 20.2 4874 66 33 33 62.7 37.3 50.0 8.5 26.0 5.2 24.0 14.0 41.4 13.1 86.9 21.6 78.4 15.3 84.7 4 1 2 0
2 Damian Lillard POR 32 36.3 32.2 9.6 20.7 46.3 4.2 11.3 37.1 8.8 9.6 91.4 0.8 4.0 4.8 7.3 3.3 0.9 0.3 1.9 49.1 16.0 2.0 1.8 119.5 117.4 2.1 33.8 2.23 20.8 2.2 11.2 6.8 9.3 56.4 64.5 33.1 99.78 17.3 4385 58 27 31 45.3 54.7 33.4 6.0 39.2 8.6 27.4 11.9 27.4 15.7 84.3 51.6 48.4 31.5 68.5 4 1 2 0
3 Shai Gilgeous-Alexander OKC 24 35.5 31.4 10.4 20.3 51.0 0.9 2.5 34.5 9.8 10.9 90.5 0.9 4.0 4.8 5.5 2.8 1.6 1.0 2.8 50.4 3.0 0.0 2.2 116.1 113.3 2.7 24.9 1.93 16.4 2.3 10.9 6.5 8.5 53.1 62.6 31.8 103.47 17.5 5211 68 33 35 87.8 12.2 60.5 9.7 8.1 12.7 31.4 17.7 50.8 20.1 79.9 31.0 69.0 21.0 79.0 4 1 2 0
4 Giannis Antetokounmpo MIL 28 32.1 31.1 11.2 20.3 55.3 0.7 2.7 27.5 7.9 12.3 64.5 2.2 9.6 11.8 5.7 3.9 0.8 0.8 3.1 54.8 46.0 6.0 5.4 116.4 109.2 7.2 31.4 1.46 16.2 6.5 26.8 17.1 11.1 57.2 60.5 37.3 103.63 20.4 4380 63 47 16 86.6 13.4 67.4 7.0 7.2 17.5 25.4 12.9 60.3 41.5 58.5 61.7 38.3 42.9 57.1 4 13 2 0
In [64]:
filtered_df.labels_3_pca.value_counts() # Look at the distribution
Out[64]:
1    217
0    109
2     90
Name: labels_3_pca, dtype: int64
In [65]:
filtered_df_new_pca = pd.DataFrame({'Player': filtered_df.Player, 'PC1': filtered_X_pca[:, 0], 'PC2': filtered_X_pca[:, 1], 'PC3': filtered_X_pca[:, 2], 'Cluster': filtered_df.labels_3_pca})
filtered_df_new_pca['Cluster'] = filtered_df_new_pca['Cluster'].astype('category')
In [66]:
fig = px.scatter(filtered_df_new_pca, x='PC1', y='PC2', color='Cluster', hover_data=['Player'],
                 title="2023 NBA Regular Filtered PCA Season Stats Clustering on 2 Components")

fig.show()
In [67]:
fig = px.scatter_3d(filtered_df_new_pca, x='PC1', y='PC2',z='PC3', color='Cluster', hover_data=['Player'],
                 title="2023 NBA Regular Filtered PCA Season Stats Clustering on 3 Components")

fig.show()

In terms of the players in each cluster, PCA and the regular filtered data aren't that different. That tells me that the players that were only playing a few minutes were causing some problems. In terms of the visualizations, PCA obviously makes it easier to see the clusters since we are looking at components and not actual variables. The interesting this is that I can see a more definitive break in the clusters. I can essentially label them. Label 2 contains your more traditional high-rebounding and blocking, lower three point shooting big men. This includes Mitchell Robinson, Rudy Gobert, Deandre Ayton, etc. Cluster 0 is your more traditional high volume players. Essentially these are the best players on teams and can often be considered superstars. This includes Luka Doncic, Devin Booker, Giannis Antetokounmpo, Nikola Jokic and many others. Cluster 1 is essentially everyone else. This includes 3 and d players (Grand Williams, Cam Johnson, Michael Porter Jr.) and other role players along with those that don't play as much. I like this because we can see the break in where players end up a little more.